A zero-one law for linear transformations of Levy noise (2009)
A L\'evy noise on $\mathbb{R}^d$ assigns a random real "mass" $\Pi(B)$ to each Borel subset $B$ of $\mathbb{R}^d$ with finite Lebesgue measure. The distribution of $\Pi(B)$ only depends on the...
DYNAMICS OF THE TIME TO THE MOST RECENT COMMON ANCESTOR IN A LARGE BRANCHING POPULATION (2009)
Abstract. If we follow an asexually reproducing population through time, then the amount of time that has passed since the most recent common ancestor (MRCA) of all current individuals lived will...
HYPERDETERMINANTAL POINT PROCESSES (2009)
Steven N. Evans, Alex Gottlieb
Abstract. As well as arising naturally in the study of non-intersecting random paths, random spanning trees, and eigenvalues of random matrices, determinantal point processes (sometimes also called...
COMMUTING BIRTH-AND-DEATH PROCESSES (2009)
Steven N. Evans, Bernd Sturmfels, Caroline Uhler
Abstract. We use methods from combinatorics and algebraic statistics to study analogues of birth-and-death processes that have as their state space a finite subset of the m-dimensional lattice and...
Spectra of large random trees (2009)
Bhamidi, Shankar, Evans, Steven N., Sen, Arnab
We analyze the eigenvalues of the adjacency matrices of a wide variety of random trees. Using general, broadly applicable arguments based on the interlacing inequalities for the eigenvalues of a...
Commuting birth-and-death processes (2008)
Evans, Steven N., Sturmfels, Bernd, Uhler, Caroline
We use methods from combinatorics and algebraic statistics to study analogues of birth-and-death processes that have as their state space a finite subset of the $m$-dimensional lattice and for which...
Dynamics of the time to the most recent common ancestor in a large branching population (2008)
Evans, Steven N., Ralph, Peter L.
If we follow an asexually reproducing population through time, then the amount of time that has passed since the most recent common ancestor (MRCA) of all current individuals lived will change as...
Vital rates from the action of mutation accumulation (2008)
Wachter, Kenneth W., Steinsaltz, David R., Evans, Steven N.
New models for evolutionary processes of mutation accumulation allow hypotheses about the age-specificity of mutational effects to be translated into predictions of heterogeneous population hazard...
The Age-Specific Force of Natural Selection and Walls of Death (2008)
Wachter, Kenneth W., Evans, Steven N., Steinsaltz, David R.
W. D. Hamilton's celebrated formula for the age-specific force of natural selection furnishes predictions for senescent mortality due to mutation accumulation, at the price of reliance on a linear...
To what extent does genealogical ancestry imply genetic ancestry? (2008)
Matsen, Frederick A., Evans, Steven N.
Recent statistical and computational analyses have shown that a genealogical most recent common ancestor (MRCA) may have lived in the recent past. However, coalescent-based approaches show that...
Hyperdeterminantal point processes (2008)
Evans, Steven N., Gottlieb, Alex
As well as arising naturally in the study of non-intersecting random paths, random spanning trees, and eigenvalues of random matrices, determinantal point processes (sometimes also called fermionic...
A generalized model of mutation-selection balance with applications to aging (2008)
David Steinsaltz, Steven N. Evans, W. Wachter
Abstract. A probability model is presented for the dynamics of mutationselection balance in a haploid infinite-population infinite-sites setting sufficiently general to cover mutation-driven changes...
Snakes and spiders: Brownian motion on R-trees (2008)
Abstract. We consider di usion processes on a class of R{trees. The processes are de ned in a manner similar to that of Le Gall's Brownian snake. Each point in the tree has a real{valued \height...
Unidentifiable divergence times in rates-across-sites models (2008)
Abstract. The rates–across–sites assumption in phylogenetic inference posits that the rate matrix governing the Markovian evolution of a character on an edge of the putative phylogenetic tree is...
FOURIER ANALYSIS AND PHYLOGENETIC TREES (2008)
Abstract. We give an overview of phylogenetic invariants: a technique for reconstructing evolutionary family trees from DNA sequence data. This method is useful in practice and is based on a number...
Luay Nakhleh, Don Ringe, Tandy Warnow, Steven N. Evans
Researchers interested in the history of the Indo-European family of languages have used a variety of methods to estimate the phylogeny of the family, and have obtained widely differing results. In...
A generalized model of mutation-selection balance with applications to aging (2008)
David Steinsaltz, Steven N. Evans, W. Wachter
Abstract. A probability model is presented for the dynamics of mutationselection balance in a haploid infinite-population infinite-sites setting sufficiently general to cover mutation-driven changes...
IMS Lecture Notes–Monograph Series (2008)
Shankar Bhamidi, Steven N. Evans, Ron Peled, Peter Ralph
Brownian motion on time scales, basic hypergeometric functions, and some continued fractions of Ramanujan
Abstract. We consider the asymptotic behavior as n → ∞ of the spectra of random matrices of the form n−1 1 � √ Znkρn((k, k + 1)), n − 1 k=1 where for each n the random variables Znk are...
François Barbançon, Y Warnow, Steven N. Evans, Donald Ringe, Luay Nakhleh
experimental study comparing linguistic phylogenetic
THE EXPECTED NUMBER OF ZEROS OF A RANDOM SYSTEM OF p-ADIC POLYNOMIALS (2008)
Abstract. We study the simultaneous zeros of a random family of d polynomials in d variables over the p-adic numbers. For a family of natural models, we obtain an explicit constant for the expected...
EMBEDDING A MARKOV CHAIN INTO A RANDOM WALK ON A PERMUTATION GROUP (2008)
Abstract. Using representation theory, we obtain a necessary and sufficient condition for a discrete–time Markov chain on a finite state space E to be representable as ΨnΨn−1 ···Ψ1z, n ≥...
DAMAGE SEGREGATION AT FISSIONING MAY INCREASE GROWTH RATES: A SUPERPROCESS MODEL (2008)
Steven N. Evans, David Steinsaltz
Abstract. A fissioning organism may purge unrepairable damage by bequeathing it preferentially to one of its daughters. Using the mathematical formalism of superprocesses, we propose a flexible class...
THE EXPECTED NUMBER OF ZEROS OF A RANDOM SYSTEM OF p-ADIC POLYNOMIALS (2008)
Abstract. We study the simultaneous zeros of a random family of d polynomials in d variables over the p-adic numbers. For a family of natural models, we obtain an explicit constant for the expected...
DIFFERENT TREES HAVE DISTINCT PHYLOGENETIC INVARIANTS (2008)
Abstract. The method of invariants is an approach to the problem of reconstructing the phylogenetic tree of a collection of m taxa using nucleotide sequence data. Models for the collection of...
DIFFUSIONS ON THE SIMPLEX FROM BROWNIAN MOTIONS ON HYPERSURFACES (2008)
Abstract. The (n, 1)-dimensional simplex is the collection of probability measures on a set with n points. Many applied situations result in simplexvalued data or in stochastic processes that have...
BALLS–IN–BOXES DUALITY FOR COALESCING RANDOM WALKS AND COALESCING BROWNIAN MOTIONS (2008)
Abstract. We present a duality relation between two systems of coalescing random walks and an analogous duality relation between two systems of coalescing Brownian motions. Our results extends...
EXPECTATION, CONDITIONAL EXPECTATION AND MARTINGALES IN LOCAL FIELDS (2008)
Abstract. We investigate a possible definition of expectation and conditional expectation for random variables with values in a local field such as the p-adic numbers. We define the expectation by...
BALLS–IN–BOXES DUALITY FOR COALESCING RANDOM WALKS AND COALESCING BROWNIAN MOTIONS (2008)
Abstract. We present a duality relation between two systems of coalescing random walks and an analogous duality relation between two systems of coalescing Brownian motions. Our results extends...
are exchangeable sequences of real{valued random variables. Suppose thatSn and (2008)
Steven N. Evans, Xiaowen Zhou, Pn Tion Considersn, Pn Sn
Abstract. Consider two exchangeable sequences (Xk)k2N and ( ^ Xk)k2N with the property that Sn P n k=1 Xk and ^ Sn P n k=1 ^ Xk have the same distribution for all n 2 N. David Aldous posed the...
STOCHASTIC BILLIARDS ON GENERAL TABLES (2008)
Abstract. We consider stochastic analogues of classical billiard systems. A particle moves at unit speed with constant direction in the interior of a bounded, d{dimensional region with continuouslydi...
ASYMPTOTIC EVOLUTION OF ACYCLIC RANDOM MAPPINGS (2008)
Abstract. An acyclic mapping from an n element set into itself is a mapping ϕ such that if ϕ k (x) = x for some k and x, then ϕ(x) = x. Equivalently, ϕ ℓ = ϕ ℓ+1 =... for ℓ sufficiently...
Abstract. We consider the elementary divisors and determinant ofauniformly distributed n n random matrix with entries in the ring of integers of an arbitrary local eld. We show that the sequence of...
Abstract. If X is a symmetric Levy process on the line, then there exists a non{decreasing, cadlag process H such thatX(H(x)) = x for all x 0 if and only if X is recurrent and has a non{trivial...
Tandy Warnow, Steven N. Evans, Don Ringe, Luay Nakhleh
ABSTRACT. We propose several models of how languages evolve, and discuss statistical estimation of evolution under these models. We also discuss issues of identifiability and statistical consistency...
Unidentifiable divergence times in rates-across-sites models (2008)
Abstract. The rates–across–sites assumption in phylogenetic inference posits that the rate matrix governing the Markovian evolution of a character on an edge of the putative phylogenetic tree is...
IMS Lecture Notes–Monograph Series (2008)
Shankar Bhamidi, Steven N. Evans, Ron Peled, Peter Ralph
Brownian motion on disconnected sets, basic hypergeometric functions, and some continued fractions of Ramanujan
The Age-Specific Force of Natural Selection and Walls of Death (2008)
Kenneth W. Wachter, Steven N. Evans, David R. Steinsaltz
W. D. Hamilton’s celebrated formula for the age-specific force of natural selection furnishes predictions for senescent mortality due to mutation accumulation, at the price of reliance on a linear...
Running head: Stationary Markov Processes (2007)
We consider some classes of stationary, counting--measure--valued Markov processes and their companions under time--reversal. Examples arise in the L'evy--Ito decomposition of stable...
Identifiability Of Exchangeable Sequences With Identically Distributed Partial Sums (2007)
Consider two exchangeable sequences (X k ) k2N and ( X k ) k2N with the property that Sn j P n k=1 X k and Sn j P n k=1 X k have the same distribution for all n 2 N. David Aldous posed the following...
Stochastic Billiards on General Tables (2007)
. We consider stochastic analogues of classical billiard systems. A particle moves at unit speed with constant direction in the interior of a bounded, d--dimensional region with...
Dirichlet Forms On Totally Disconnected Spaces And Bipartite Markov Chains (2007)
. We use Dirichlet form methods to construct and analyse a general class of reversible Markov processes with totally disconnected state spaces. We study in detail the special case of bipartite Markov...
Local Fields, Gaussian Measures, And Brownian Motions (2007)
this paper has not been published, but some of its essence can be gleaned from [Madrecki, 1985, 1990, 1991].) The resulting theory is similar in many ways to the Euclidean theory. For example, linear...
EMBEDDING A MARKOV CHAIN INTO A RANDOM WALK ON A PERMUTATION GROUP (2007)
Abstract. Using representation theory, we obtain a necessary and su#cient condition for a discrete--time Markov chain on a finite state space E to be representable as #n#n-1
Markov processes on vermiculated spaces (2007)
Martin T. Barlow, Steven N. Evans
Abstract. A general technique is given for constructing new Markov processes from existing ones. The new process and its state space are both projective limits of sequences built by an iterative...
FOURIER ANALYSIS AND PHYLOGENETIC TREES (2007)
Abstract. We give an overview of phylogenetic invariants: a technique for reconstructing evolutionary family trees from DNA sequence data. This method is useful in practice and is based on a number...
Minimax Expected Measure Confidence Sets for (2007)
Restricted Location Parameters, Steven N. Evans, Bendek B. Hansen, Philip B. Stark
This paper studies how to construct confidence sets that are as small as they can be, in the sense of minimizing worst-case expected measure, while attaining at least their nominal confidence level....
Clayton, Aubrey, Evans, Steven N.
We study a continuous-time dynamical system that models the evolving distribution of genotypes in an infinite population where genomes may have infinitely many or even a continuum of loci, mutations...
We consider the asymptotic behavior as $n \to \infty$ of the spectra of random matrices of the form \[\frac{1}{\sqrt{n-1}} \sum_{k=1}^{n-1} Z_{nk} \rho_n((k,k+1)),\] where for each $n$ the random...
Expectation, Conditional Expectation and Martingales in Local Fields (2007)
Evans, Steven N.; University Of California At Berkeley; Evans@stat.berkeley.edu, Lidman, Tye; University Of California At Berkeley; Tlid@berkeley.edu
We investigate a possible definition of expectation and conditional expectation for random variables with values in a local field such as the p-adic numbers. We define the expectation by analogy with...
Expectation, Conditional Expectation and Martingales in Local Fields (2007)
Evans, Steven N.; University Of California At Berkeley; Evans@stat.berkeley.edu, Lidman, Tye; University Of California At Berkeley; Tlid@berkeley.edu
We investigate a possible definition of expectation and conditional expectation for random variables with values in a local field such as the p-adic numbers. We define the expectation by analogy with...
Asymptotic evolution of acyclic random mappings (2007)
An acyclic mapping from an $n$ element set into itself is a mapping $\phi$ such that if $\phi^k(x) = x$ for some $k$ and $x$, then $\phi(x) = x$. Equivalently, $\phi^\ell = \phi^{\ell+1} = ...$ for...
The expected number of zeros of a random system of p-adic polynomials (2006)
Evans, Steven N.; University Of California At Berkeley; Evans@stat.berkeley.edu
We study the simultaneous zeros of a random family of d polynomials in d variables over the p-adic numbers.For a family of natural models, we obtain an explicit constant for the expected number of...
A mutation-selection model for general genotypes with recombination (2006)
Evans, Steven N., Steinsaltz, David, Wachter, Kenneth W.
A probability model is presented for the dynamics of mutation-selection balance in a infinite-population infinite-sites setting sufficiently general to cover mutation-driven changes in full...
Damage segregation at fissioning may increase growth rates: A superprocess model (2006)
Evans, Steven N., Steinsaltz, David
A fissioning organism may purge unrepairable damage by bequeathing it preferentially to one of its daughters. Using the mathematical formalism of superprocesses, we propose a flexible class of...
Expectation, Conditional Expectation and Martingales in Local Fields (2006)
We investigate a possible definition of expectation and conditional expectation for random variables with values in a local field such as the $p$-adic numbers. We define the expectation by analogy...
Subtree prune and regraft: A reversible real tree-valued Markov process (2006)
Evans, Steven N., Winter, Anita
We use Dirichlet form methods to construct and analyze a reversible Markov process, the stationary distribution of which is the Brownian continuum random tree. This process is inspired by the subtree...
Non-equilibrium theory of the allele frequency spectrum (2006)
Evans, Steven N., Shvets, Yelena, Slatkin, Montgomery
A forward diffusion equation describing the evolution of the allele frequency spectrum is presented. The influx of mutations is accounted for by imposing a suitable boundary condition. For a...
The expected number of zeros of a random system of $p$-adic polynomials (2006)
We study the simultaneous zeros of a random family of $d$ polynomials in $d$ variables over the $p$-adic numbers. For a family of natural models, we obtain an explicit constant for the expected...
Steven N. Evans, Yelena Shvets, Montgomery Slatkin
Abstract. A forward diffusion equation describing the evolution of the allele frequency spectrum is presented. The influx of mutations is accounted for by imposing a suitable boundary condition. For...
Steven N. Evans, Yelena Shvets, Montgomery Slatkin
Abstract. A forward diffusion equation describing the evolution of the allele frequency spectrum is presented. The influx of mutations is accounted for by imposing a suitable boundary condition. For...
Subtree prune and regraft: a reversible real tree-valued Markov process (2006)
Abstract. We use Dirichlet form methods to construct and analyze a reversible Markov process, the stationary distribution of which is the Brownian continuum random tree. This process is inspired by...
A stochastic model of language evolution that incorporates homoplasy and borrowing (2006)
Tandy Warnow, Steven N. Evans, Donald Ringe
The inference of evolutionary history, whether in biology or in linguistics, is aided by a carefully considered model of the evolutionary process and a reconstruction method which is expected to...
A stochastic model of language evolution that incorporates homoplasy and borrowing (2006)
Tandy Warnow, Steven N. Evans, Donald Ringe
The inference of evolutionary history, whether in biology or in linguistics, is aided by a carefully considered model of the evolutionary process and a reconstruction method which is expected to...
Subtree prune and regraft: a reversible real tree-valued Markov process (2006)
Abstract. We use Dirichlet form methods to construct and analyze a reversible Markov process, the stationary distribution of which is the Brownian continuum random tree. This process is inspired by...
A stochastic model of language evolution that incorporates homoplasy and borrowing (2006)
Tandy Warnow, Steven N. Evans, Donald Ringe
The inference of evolutionary history, whether in biology or in linguistics, is aided by a carefully considered model of the evolutionary process and a reconstruction method which is expected to...
Matsen, Frederick A., Evans, Steven N.
There are several common ways to encode a tree as a matrix, such as the adjacency matrix, the Laplacian matrix (that is, the infinitesimal generator of the natural random walk), and the matrix of...
Bhamidi, Shankar, Evans, Steven N., Peled, Ron, Ralph, Peter
Motivated by L\'{e}vy's characterization of Brownian motion on the line, we propose an analogue of Brownian motion that has as its state space an arbitrary closed subset of the line that is unbounded...
Minimax expected measure confidence sets for restricted location parameters (2005)
Evans, Steven N., Hansen, Ben B., Stark, Philip B.
We study confidence sets for a parameter θ∈Θ that have minimax expected measure among random sets with at least 1-α coverage probability. We characterize the minimax sets using duality, which...
Subtree prune and regraft: a reversible real tree-valued Markov process (2005)
Evans, Steven N., Winter, Anita
We use Dirichlet form methods to construct and analyze a reversible Markov process, the stationary distribution of which is the Brownian continuum random tree. This process is inspired by the subtree...
A comparison of phylogenetic reconstruction methods on an IE dataset (2005)
Luay Nakhleh, Tandy Warnow, Don Ringe, Steven N. Evans
Researchers interested in the history of the Indo-European family of languages have used a variety of methods to estimate the phylogeny of the family, and have obtained widely differing results. In...
A comparison of phylogenetic reconstruction methods on an IE dataset (2005)
Luay Nakhleh, Tandy Warnow, Don Ringe, Steven N. Evans
Researchers interested in the history of the Indo-European family of languages have used a variety of methods to estimate the phylogeny of the family, and have obtained widely differing results. In...
Minimax expected measure confidence sets for restricted location parameters (2005)
Steven N. Evans, Bendek B. Hansen
We study confidence sets for a parameter θ ∈ Θ that have minimax expected measure among random sets with at least 1 − α coverage probability. We
A comparison of phylogenetic reconstruction methods on an IE dataset (2005)
Luay Nakhleh, Tandy Warnow, Don Ringe, Steven N. Evans
Researchers interested in the history of the Indo-European family of languages have used a variety of methods to estimate the phylogeny of the family, and have obtained widely differing results. In...
Unidentifiable divergence times in rates-across-sites models (2004)
Evans, Steven N., Warnow, Tandy
The rates-across-sites assumption in phylogenetic inference posits that the rate matrix governing the Markovian evolution of a character on an edge of the putative phylogenetic tree is the product of...
Balls-in-boxes duality for coalescing random walks and coalescing Brownian motions (2004)
Evans, Steven N., Zhou, Xiaowen
We present a duality relation between two systems of coalescing random walks and an analogous duality relation between two systems of coalescing Brownian motions. Our results extends previous work in...
Quasistationary distributions for one-dimensional diffusions with killing (2004)
Steinsaltz, David, Evans, Steven N.
We extend some results on the convergence of one-dimensional diffusions killed at the boundary, conditioned on extended survival, to the case of general killing on the interior. We show, under fairly...
A generalized model of mutation-selection balance with applications to aging (2004)
Steinsaltz, David, Evans, Steven N., Wachter, Kenneth W.
A probability model is presented for the dynamics of mutation-selection balance in a haploid infinite-population infinite-sites setting sufficiently general to cover mutation-driven changes in full...
Rayleigh processes, real trees, and root growth with re-grafting (2004)
Evans, Steven N., Pitman, Jim, Winter, Anita
The real trees form a class of metric spaces that extends the class of trees with edge lengths by allowing behavior such as infinite total edge length and vertices with infinite branching degree....
Markov Mortality Models: Implications Of Quasistationarity And Varying Initial Distributions (2004)
David Steinsaltz, Steven N. Evans
This paper explains some implications of markov-process theory for models of mortality. We show that an important qualitative feature which has been found in certain models --- the convergence to a...
Rayleigh processes, real trees, and root growth with re-grafting (2004)
Steven N. Evans, Steven N. Evans, Jim Pitman, Jim Pitman, Anita Winter, Anita Winter
Abstract. The real trees form a class of metric spaces that extends the class of trees with edge lengths by allowing behavior such as infinite total edge length and vertices with infinite branching...
Inference of divergence times as a statistical inverse problem (2004)
Steven N. Evans, Don Ringe, Tandy Warnow
A familiar complaint about statisticians and applied mathematicians is that they are the possessors of a relatively small number of rather elegant hammers with which they roam the world seeking...
Inference of divergence times as a statistical inverse problem (2004)
Steven N. Evans, Don Ringe, Tandy Warnow
A familiar complaint about statisticians and applied mathematicians is that they are the possessors of a relatively small number of rather elegant hammers with which they roam the world seeking...
Pinching and twisting Markov processes (2003)
Evans, Steven N., Sowers, Richard B.
We develop a technique for "partially collapsing'' one Markov process to produce another. The state space of the new Markov process is obtained by a pinching operation that identifies points of the...
Minimax Expected Measure Confidence Sets for Restricted Location Parameters (2003)
Steven N. Evans, Bendek B. Hansen, Philip B. Stark
This paper studies how to construct confidence sets that are as small as they can be, in the sense of minimizing worst-case expected measure, while attaining at least their nominal confidence level....
Estimating some features of $NK$ fitness landscapes (2002)
Evans, Steven N., Steinsaltz, David
Kauffman and Levin introduced a class of models for the evolution of hereditary systems which they called $NK$ fitness landscapes. Inspired by spinglasses, these models have the attractive feature of...
Estimating some features of NK fitness landscapes (2002)
Steven N. Evans, David Steinsaltz
Stuart Kauffman introduced a class of models for the evolution of hereditary systems which he called "NK fitness landscapes". Inspired by spinglasses, these models have the...
Inverse problems as statistics (2002)
Abstract. What mathematicians, scientists, engineers, and statisticians mean by "inverse problem " differs. For a statistician, an inverse problem is an inference or estimation...
Inverse problems as statistics (2002)
Abstract. What mathematicians, scientists, engineers, and statisticians mean by \inverse problem " di ers. For a statistician, an inverse problem is an inference or estimation problem. The...
Eigenvalues of random wreath products (2002)
Abstract. Consider a unifomrly chosen element Xn of the n-fold wreath product \Gamma n = G o G o \Delta \Delta \Delta o G, where G is a finite permutation group acting transitively on some set of...
Eigenvalues of random wreath products (2002)
Abstract. Consider a uniformly chosen element Xn of the n-fold wreath product,n = G o G o oG, whereG is a nite permutation group acting transitively on some set of size s. The eigenvalues ofXn in the...
Inverse problems as statistics (2002)
Abstract. What mathematicians, scientists, engineers, and statisticians mean by \inverse problem " di ers. For a statistician, an inverse problem is an inference or estimation problem. The...
Inverse problems as statistics (2002)
Abstract. What mathematicians, scientists, engineers, and statisticians mean by \inverse problem " di ers. For a statistician, an inverse problem is an inference or estimation problem. The...
Estimating some features of NK fitness landscapes (2002)
Steven N. Evans, David Steinsaltz
Abstract. Kau man and Levin (1987) introduced a class of models for the evolution of hereditary systems which they called \NK tness landscapes". Inspired by spinglasses, these models have...
Eigenvalues of Random Wreath Products (2001)
Evans, Steven N.; University Of California At Berkeley; Evans@stat.berkeley.edu
Consider a uniformly chosen element $X_n$ of the $n$-fold wreath product $Gamma_n = G wr G wr cdots wr G$, where $G$ is a finite permutation group acting transitively on some set of size $s$....
Stochastic billiards on general tables (2001)
We consider stochastic analogs of classical billiard systems. A particle moves at unit speed with constant direction in the interior of a bounded, d-dimensional region with continuously...
Pinching and twisting Markov processes (2001)
Abstract. We develop a technique for \partially collapsing " one Markovprocesses to produce another. The state space of the new Markov process is obtained by a pinching operation that identi...
Continuum-sites stepping-stone models, coalescing exchangeable partitions and random trees (2000)
Donnelly, Peter, Evans, Steven N., Fleischmann, Klaus, Kurtz, Thomas G., Zhou, Xiaowen
Analogues of stepping-stone models are considered where the sitespace is continuous, the migration process is a general Markov process, and the type-space is infinite. Such processes were defined in...
Immanants And Finite Point Processes (2000)
Persi Diaconis, STEVEN N. EVANS, In This Case
. Given a Hermitian, non-negative definite kernel K and a character of the symmetric group on n letters, define the corresponding immanant function K [x 1 ; : : : ; xn ] := P oe (oe) Q n i=1 K(x i ;...
Linear Functionals Of Eigenvalues Of Random Matrices (2000)
Persi Diaconis, Steven N. Evans
. Let Mn be a random n \Theta n unitary matrix with distribution given by Haar measure on the unitary group. Using explicit moment calculations, a general criterion is given for linear combinations...
Identifiability of Exchangeable Sequences with Identically Distributed Partial Sums (1999)
Evans, Steven N.; University Of California At Berkeley; Evans@stat.berkeley.edu, Zhou, Xiaowen; University Of California At Berkeley; Xzhou@stat.berkeley.edu
Consider two exchangeable sequences $(X_k)_{k in bN}$ and $(hat{X}_k)_{k in bN}$ with the property that $S_n equiv sum_{k=1}^n X_k$ and $hat{S}_n equiv sum_{k=1}^n hat{X}_k$ have the same...
Right Inverses Of Lévy Processes And Stationary Stopped Local Times (1999)
. If X is a symmetric L'evy process on the line, then there exists a non--decreasing, c`adl`ag process H such that X(H(x)) = x for all x 0 if and only if X is recurrent and has a non--trivial...
Snakes And Spiders: Brownian Motion On R-Trees (1999)
Steven N. Evans, Steven N. Evans
. We consider diffusion processes on a class of R--trees. The processes are defined in a manner similar to that of Le Gall's Brownian snake. Each point in the tree has a real--valued...
Continuum-sites stepping-stone models, coalescing exhcangeable partitions, and random trees (1998)
Donnelly, Peter, Evans, Steven N., Fleischmann, Klaus, Kurtz, Thomas G., Zhou, Xiaowen
Analogues of stepping--stone models are considered where the site--space is continuous, the migration process is a general Markov process, and the type--space is infinite. Such processes were defined...
Eventual Intersection for Sequences of Lévy Processes (1998)
Evans, Steven N.; University Of California At Berkeley; Evans@stat.berkeley.edu, Peres, Yuval; University Of California, Berkeley; Peres@stat.berkeley.edu
Consider the events ${F_n cap bigcup_{k=1}^{n-1} F_k = emptyset}$, $n in N$, where $(F_n)_{n=1}^infty$ is an i.i.d. sequence of stationary random subsets of a compact group $G$. A plausible...
Collision Local Times, Historical Stochastic Calculus, and Competing Species (1998)
Evans, Steven N.; University Of California At Berkeley; Evans@stat.berkeley.edu, Perkins, Edwin A.; The University Of British Columbia; Perkins@math.ubc.ca
Branching measure-valued diffusion models are investigated that can be regarded as pairs of historical Brownian motions modified by a competitive interaction mechanism under which individuals from...
Local fields, Gaussian measures, and Brownian motions (1998)
These are lecture notes from a course given at the CRM in Montreal in 1992. They survey the author's attempts to find and understand canonical probabilistic entities in a local field (e.g. p-adic)...
Transition operators of diffusions reduce zero-crossing (1998)
Evans, Steven N., Williams, Ruth J.
If $u(t,x)$ is a solution of a one--dimensional, parabolic, second--order, linear partial differential equation (PDE), then it is known that, under suitable conditions, the number of zero--crossings...
Construction of Markovian coalescents (1998)
Partition-valued and measure-valued coalescent Markov processes are constructed whose state describes the decomposition of a finite total mass m into a finite or countably infinite number of masses...
Transition Operators Of Diffusions Reduce Zero-Crossing (1998)
Steven N. Evans, Ruth J. Williams, J. Williams
. If u(t; x) is a solution of a one--dimensional, parabolic, second--order, linear partial differential equation (PDE), then it is known that, under suitable conditions, the number of zero--crossings...
Constructing and counting phylogenetic invariants (1998)
Abstract. The method of invariants is an approach to the problem of reconstructing the phylogenetic tree of a collection of m taxa using nucleotide sequence data. Models for the respective...
Random spanning trees of Cayley graphs and an associated compacti cation of semigroups (1998)
A sequential construction of a random spanning tree for the Cay-ley graph of a nitely generated, countably in nite subsemigroup V of a group G is considered. At stagen, the spanning tree T is...
Eventual intersection of sequences of Lévy processes (1998)
Abstract: Consider the events fFn \ S n,1 k=1 Fk =;g, n 2 N, where (Fn) 1 n=1 is an i.i.d. sequence of stationary random subsets of a compact group G. A plausible conjecture is that these events will...
Transition operators of di usions reduce zero{crossing (1998)
If u(t; x) is a solution of a one{dimensional, parabolic, second{order, linear partial di erential equation (PDE), then it is known that, under suitable conditions, the number of zero{crossings of...
Construction of Markovian coalescents (1998)
Partition-valued and measure-valued coalescent Markov processes are constructed whose state describes the decomposition of a nite total mass m into a nite or countably in nite number of masses with...
Continuum-sites steppingstone models, coalescing exchangeable partitions, and random (1998)
Peter Donnelly, Steven N. Evans, Klaus Fleischmann, Thomas G. Kurtz, Xiaowen Zhou
Analogues of stepping-stone models are considered where the sitespace is continuous, the migration process is a general Markov process, and the type-space is infinite. Such processes were defined in...
Stopped Markov chains with stationary occupation (1997)
Abstract: Let E be a finite set equipped with a group G of bijective transformations and suppose that X is an irreducible Markov chain on E that is equivariant under the action of G. In particular,...
We consider some classes of stationary, counting{measure{valued Markov processes and their companions under time{reversal. Examples arise in the Levy{It^o decomposition of stable Ornstein{Uhlenbeck...
Stopped Markov chains with stationary occupation (1997)
Abstract: Let E be a nite set equipped with a group G of bijective transformations and suppose that X is an irreducible Markov chain on E that is equivariant under the action of G. In particular, if...
Collision local times, historical stochastic calculus, and (1997)
competing superprocesses
Infinitely-many-species Lotka-Volterra equations arising from systems of coalescing masses (1997)
We consider nonlinear, probability measure{valued dynamical systems that generalise those classical Lotka{Volterra equations in which, to use ecological terminology, the total size of a nite number...
Cluster formation in a stepping-stone model with continuous, hierarchically structured sites (1996)
Evans, Steven N., Fleischmann, Klaus
A stepping-stone model with site space a continuous, hierarchical group is constructed via duality with a system of (delayed) coalescing "stable" Lévy processes. This model can be understood as a...
Shrinkage estimators, Skorokhod's problem and stochastic integration by parts (1996)
Evans, Steven N., Stark, Philip B.
For a broad class of error distributions that includes the spherically symmetric ones, we give a short proof that the usual estimator of the mean in a d-dimensional shift model is inadmissible under...
Cluster Formation in a Stepping Stone Model With Continuous, Hierarchically Structured Sites (1995)
Steven N. Evans, Klaus Fleischmann
A stepping stone model with site space a continuous, hierarchical group is constructed via duality with a system of (delayed) coalescing "stable" L'evy processes. This model can be...
Association and infinite divisibility for the Wishart distribution and its diagonal marginals
We give an example of a central Wishart matrix W with one degree of freedom and scale matrix of rank 2 such that the diagonal entries of W are not associated. This allows us to conclude that no...