Robin Pemantle

A survey of random processes with reinforcement (2007)

Consider a binary tree, to the vertices of which are assigned independent Bernoulli random variables with mean p

Quantum random walks in one dimension via generating functions (2007)

The models surveyed include generalized Pólya urns, reinforced random walks, interacting urn models, and continuous reinforced processes. Emphasis is on methods and results, with sketches provided...

Andrew Bressler, Robin Pemantle

We analyze nearest neighbor one-dimensional quantum random walks with arbitary unitary coin-flip matrices. Using a multivariate generating function analysis we give a simplified proof of a known...

When is 0.999... equal to 1 (2007)

Robin Pemantle, Carsten Schneider

The three dots in the title do not refer to an infinite sequence of 9’s, but to digits that are increasingly hard to compute. The question is philosophical: how many 9’s do we need to see before...

When is 0.999... equal to 1 (2007)

Robin Pemantle, Carsten Schneider

The three dots in the title do not refer to an infinite sequence of 9’s, but to digits that are increasingly hard to compute. The question is philosophical: how many 9’s do we need to see before...

When is 0.999... equal to 1 (2007)

Robin Pemantle, Carsten Schneider

Abstract. A doubly infinite sum, numerically evaluated at between 0.999 and 1.001, turns out to have a nice value. 1.

A survey of random processes with reinforcement (2006)

Twenty combinatorial examples of asymptotics derived from multivariate generating functions (2005)

The models surveyed include generalized P\'{o}lya urns, reinforced random walks, interacting urn models, and continuous reinforced processes. Emphasis is on methods and results, with sketches...

Pemantle, Robin, Wilson, Mark C.

Let $\{a_\rr : \rr \in (\Z^+)^d \}$ be a $d$-dimensional array of numbers, for which the generating function $F(\zz) := \sum_\rr a_\rr \zz^\rr$ is meromorphic in a neighborhood of the origin. For...

Learning to Network (2005)

The Klee-Minty random edge chain moves with linear speed (2005)

Balogh, Jozsef, Pemantle, Robin

An infinite sequence of 0's and 1's evolves by flipping each~1 to a~0 exponentially at rate one. When a~1 flips, all bits to its right also flip. Starting from any configuration with finitely many...

The critical Ising model on trees, concave recursions and nonlinear capacity (2005)

Economic properties of social networks (2005)

We consider the Ising model on a general tree under various boundary conditions: all plus, free and spin-glass. In each case, we determine when the root is influenced by the boundary values in the...

Sham M. Kakade, Michael Kearns, Luis E. Ortiz, Robin Pemantle, Siddharth Suri

We examine the marriage of recent probabilistic generative models for social networks with classical frameworks from mathematical economics. We are particularly interested in how the statistical...

Economic properties of social networks (2005)

Sham M. Kakade, Michael Kearns, Luis E. Ortiz, Robin Pemantle, Siddharth Suri

We examine the marriage of recent probabilistic generative models for social networks with classical frameworks from mathematical economics. We are particularly interested in how the statistical...

Series Twenty Combinatorial Examples of Asymptotics Derived From Multivariate Generating Functions (2005)

Robin Pemantle, Mark C. Wilson

Department of Computer Science,

Economic properties of social networks (2005)

Sham M. Kakade, Michael Kearns, Luis E. Ortiz, Robin Pemantle, Siddharth Suri

We examine the marriage of recent probabilistic generative models for social networks with classical frameworks from mathematical economics. We are particularly interested in how the statistical...

More rigorous results on the Kauffman–Levin model of evolution (2004)

Limic, Vlada, Pemantle, Robin

The purpose of this note is to provide proofs for some facts about the NK model of evolution proposed by Kauffman and Levin. In the case of normally distributed fitness summands, some of these facts...

Asymptotics of multivariate sequences, II: multiple points of the singular variety (2004)

Pemantle, Robin, Wilson, Mark

We consider a multivariate generating function F(z), whose coefficients are indexed by d-tuples of nonnegative integers: F(z) = sum_r a_r z^r where z^r denotes the product of z_j^{r_j} over j = 1,...

Irreducible compositions and the first return to the origin of a random walk (2004)

Bender, Edward A., Lawler, Gregory F., Pemantle, Robin, Wilf, Herbert S.

Let $n = b_1 + ... + b_k = b_1' + \cdot + b_k'$ be a pair of compositions of $n$ into $k$ positive parts. We say this pair is {\em irreducible} if there is no positive $j < k$ for which $b_1 + ......

Conceptual Proofs of L log L Criteria (2004)

Lyons, Russell, Pemantle, Robin, Peres, Yuval

The Kesten-Stigum Theorem is a fundamental criterion for the rate of growth of a supercritical branching process, showing that an L log L condition is decisive. In critical and subcritical cases,...

Maximum Variation of Total Risk (2004)

Random Walks in Varying Dimensions (2004)

Let Z>0 be a random time. The total risk of discovering Z in the next time interval (t,t+dt) is never more variable than an exponential of mean one, which is achieved when the information up to time...

On which graphs are all random walks in random environments transient? (2004)

We establish recurrence criteria for sums of independent random variables which take values in Euclidean lattices of varying dimension. In particular, we describe transient inhomogenous random walks...

The trace of spatial Brownian motion is capacity-equivalent to the unit square (2004)

An infinite graph G has the property that a random walk in random environment on G defined by i.i.d. resistances with any common distribution is almost surely transient, if and only if for some p

Pemantle, Robin, Peres, Yuval, Shapiro, Jonathan W.

We show that with probability 1, the trace B[0,1] of Brownian motion in space, has positive capacity with respect to exactly the same kernels as the unit square. More precisely, the energy of...

Diffusion limited aggregation on a tree (2004)

Barlow, MArtin T., Pemantle, Robin, Perkins, Edwin A.

We study the following growth model on a regular d-ary tree. Points at distance n adjacent to the existing subtree are added with probabilities proportional to alpha^{-n}, where alpha=1. Results are...

Sharpness of second moment criteria for branching and tree-indexed processes (2004)

On near-critical and dynamical percolation in the tree case (2004)

A class of branching processes in varying environments is exhibited which become extinct almost surely even though the means M_n grow fast enough so that sum M_n^{-1} is finite. In fact, such a...

Haggstrom, Olle, Pemantle, Robin

Consider independent bond percolation with retention probability p on a spherically symmetric tree Gamma. Write theta_Gamma(p) for the probability that the root is in an infinite open cluster, and...

Robust Phase Transitions for Heisenberg and Other Models on General Trees (2004)

Pemantle, Robin, Steif, Jeffrey E.

We study several statistical mechanical models on a general tree. Particular attention is devoted to the classical Heisenberg models, where the state space is the d-dimensional unit sphere and the...

Moment conditions for a sequence with negative drift to be uniformly bounded in L^r (2004)

Pemantle, Robin, Rosenthal, Jeffrey S.

Suppose a sequence of random variables {X_n} has negative drift when above a certain threshold and has increments bounded in L^p. When p>2 this implies that EX_n is bounded above by a constant...

Sojourn times for Brownian sheet (2004)

Khoshnevisan, Davar, Pemantle, Robin

This paper is dedicated to Professor Endre Csakion the occasion of his 65th birthday.

Towards a theory of negative dependence (2004)

Non-amenable products are not treeable (2004)

The FKG theorem says that the POSITIVE LATTICE CONDITION, an easily checkable hypothesis which holds for many natural families of events, implies POSITIVE ASSOCIATION, a very useful property. Thus...

Where did the Brownian particle go? (2004)

Let X and Y be infinite graphs, such that the automorphism group of X is nonamenable, and the automorphism group of Y has an infinite orbit. We prove that there is no automorphism-invariant measure...

Pemantle, Robin, Peres, Yuval, Pitman, Jim, Yor, Marc

Consider the radial projection onto the unit sphere of the path a d-dimensional Brownian motion W, started at the center of the sphere and run for unit time. Given the occupation measure mu of this...

A phase transition in random coin tossing (2004)

Levin, David A., Pemantle, Robin, Peres, Yuval

Suppose that a coin with bias theta is tossed at renewal times of a renewal process, and a fair coin is tossed at all other times. Let mu_\theta be the distribution of the observed sequence of coin...

Uniform random spanning trees (2004)

Tree-indexed processes (2004)

There are several good reasons you might want to read about uniform spanning trees, one being that spanning trees are useful combinatorial objects. Not only are they fundamental in algebraic graph...

A Dynamic Model of Social Network Formation (2004)

This article examines a recent body of work on stochastic processes indexed by a tree. Emphasis is on the application of this new framework to existing probability models. Proofs are largely omitted,...

Cycles in random k-ary maps and the poor performance of random random number generation (2004)

We consider a dynamic social network model in which agents play repeated games in pairings determined by a stochastically evolving social network. Individual agents begin to interact at random, with...

A probabilistic model for the degree of the cancellation polynomial in Gosper's Algorithm (2004)

Knuth shows that iterations of a random function perform poorly on average as a random number generator. He proposes a generalization in which the next value depends on two or more previous values....

What is the probability of intersecting the set of Brownian double points? (2004)

Milenkovic and Compton in 2002 gave an analysis of the run time of Gosper's algorithm applied to a random input. The main part of this was an asymptotic analysis of the random degree of the...

Network formation by reinforcement learning: the long and medium run (2004)

We give potential theoretic estimates for the probability that a set $A$ contains a double point of planar Brownian motion run for unit time. Unlike the probability for $A$ to intersect the range of...

Pemantle, Robin, Skyrms, Brian

We investigate a simple stochastic model of social network formation by the process of reinforcement learning with discounting of the past. In the limit, for any value of the discounting parameter,...

Time to absorption in discounted reinforcement models (2004)

Pemantle, Robin, Skyrms, Brian

Reinforcement schemes are a class of non-Markovian stochastic processes. Their non-Markovian nature allows them to model some kind of memory of the past. One subclass of such models are those in...

Vertex-Reinforced Random Walk (2004)

Critical RWRE on trees and tree-indexed random walks (2004)

This paper considers a class of non-Markovian discrete-time random processes on a finite state space {1,...,d}. The transition probabilities at each time are influenced by the number of times each...

Choosing a Spanning Tree for the Integer Lattice Uniformly (2004)

We study the behavior of Random Walk in Random Environment (RWRE) on trees in the critical case left open in previous work. Representing the random walk by an electrical network, we assume that the...

Domination Between Trees and Application to an Explosion Problem (2004)

Consider the nearest neighbor graph for the integer lattice Z^d in d dimensions. For a large finite piece of it, consider choosing a spanning tree for that piece uniformly among all possible...

Random Walk in a Random Environment and First-Passage Percolation on Trees (2004)

We define a notion of stochastic domination between trees, where one tree dominates another if when the vertices of each are labeled with independent, identically distributed random variables, one...

Pemantle, Robin, Lyons, Russell

We show that the transience or recurrence of a random walk in certain random environments on an arbitrary infinite locally finite tree is determined by the branching number of the tree, which is a...

The Contact Process on Trees (2004)

On Path Integrals for the High-Dimensional Brownian Bridge (2004)

The contact process on an infinite homogeneous tree is shown to exhibit at least two phase transitions as the infection parameter lambda is varied. For small values of lambda a single infection...

Pemantle, Robin, Penrose, Mathew

Let v be a bounded function with bounded support in R^d, d>=3. Let x,y in R^d. Let Z(t) denote the path integral of v along the path of a Brownian bridge in R^d which runs for time t, starting at x...

Local Characteristics, Entropy and Limit Theorems for Spanning Trees and Domino Tilings via Transfer-Impedances (2004)

Burton, Robert, Pemantle, Robin

Let G be a finite graph or an infinite graph on which Z^d acts with finite fundamental domain. If G is finite, let T be a random spanning tree chosen uniformly from all spanning trees of G; if G is...

Critical Random Walk in Random Environment on Trees of Exponential Growth (2004)

Planar first-passage percolation times are not tight (2004)

This paper studies the behavior of RWRE on trees in the critical case left open in previous work. For trees of exponential growth, a random perturbation of the transition probabilities can change a...

A Shuffle that Mixes Sets of any Fixed Size much Faster than it Mixes the Whole Deck (2004)

We consider first-passage percolation on the two-dimensional integer lattice Z^2 with passage times that are IID exponentials of mean one. It has been conjectured, based on numerical evidence, that...

Galton-Watson Trees with the Same Mean Have the Same Polar Sets (2004)

Consider an n by n array of cards shuffled in the following manner. An element x of the array is chosen uniformly at random; Then with probability 1/2 the rectangle of cards above and to the left of...

Martin Capacity for Markov Chains (2004)

Evans defines a notion of what it means for a set B to be polar for a process indexed by a tree. The main result herein is that a tree picked from a Galton-Watson measure whose offspring distribution...

Percolation, first-passage percolation, and covering times for Richardson's model on the n-cube (2004)

The probability that a transient Markov chain, or a Brownian path, will ever visit a given set Lambda, is classically estimated using the capacity of Lambda with respect to the Green kernel G(x,y)....

Fill, James Allen, Pemantle, Robin

Percolation with edge-passage probability p and first-passage percolation are studied for the n-cube B_n ={0,1}^n with nearest neighbor edges. For oriented and unoriented percolation, p=e/n and p=1/n...

Asymptotics of multivariate sequences. II. Multiple points of the singular variety (2004)

Robin Pemantle, C. Wilson

r arzr be a multivariate generating function which is meromorphic in some neighborhood of the origin of C d, and let V be its set of singularities. Effective asymptotic expansions for the...

Common intervals of permutations (2004)

Sylvie Corteel, Guy Louchard, Robin Pemantle

An interval of a permutation is a consecutive substring consisting of consecutive symbols. For example, 4536 is an interval in the permutation 71453682. These arise in genetic applications. For the...

Convolutions of inverse linear functions via multivariate residues (2004)

Yuliy Baryshnikov, Robin Pemantle

lj(z1,...,zd) n j be the quotient of an analytic function by a product of linear functions lj: = 1 − � bijzi. We compute asymptotic formulae for the Taylor coefficients of F via the multivariate...

Asymptotics of multivariate sequences. II. Multiple points of the singular variety (2004)

Markc Wilson, Robin Pemantle, Robin Pemantle, C. Wilson

Abstract. Let F (z) = � r arzr be a multivariate generating function which is meromorphic in some neighborhood of the origin of C d,andletV be its set of singularities. Effective asymptotic...

Common Intervals in Permutations (2004)

Sylvie Corteel, Guy Louchard, Robin Pemantle

An interval of a permutation is a consecutive substring consisting of consectuve symbols. For example, 4536 is an interval in the permutation 71453682. These arise in genetic applications. For the...

More rigorous results on the Kauffman-Levin model of evolution (2003)

Limic, Vlada, Pemantle, Robin

The purpose of this note is to provide proofs for some facts about the NK model of evolution proposed by Kauffman and Levin. In the case of normally distributed fitness summands, some of these facts...

Network formation by reinforcement learning: the long and medium run (2003)

Robin Pemantle, Brian Skyrms

We investigate a simple stochastic model of social network formation by the process of reinforcement learning with discounting of the past. In the limit, for any value of the discounting parameter,...

Network formation by reinforcement learning: the long and medium run (2003)

Robin Pemantle, Brian Skyrms

We investigate a simple stochastic model of social network formation by the process of reinforcement learning with discounting of the past. In the limit, for any value of the discounting parameter,...

Time to Absorption in Discounted Reinforcement Models (2003)

Robin Pemantle, Brian Skyrms

Reinforcement schemes are a class of non-Markovian stochastic processes. Their non-Markovian nature allows them to model some kind of memory of the past. One subclass of such models are those in...

More rigorous results on the NK model (2003)

Vlada Limic Robin, Robin Pemantle

The purpose of this note is to provide proofs for some facts about the NK model. In the case of normally distributed tness summands, some of these facts have been previously conjectured and...

Generating A Random Sink-Free Orientation In (2002)

Quadratic Time Henry, Henry Cohn, Robin Pemantle, James Propp

A sink-free orientation of a nite undirected graph is a choice of orientation for each edge such that every vertex has out-degree at least 1. Bubley and Dyer (1997) use Markov Chain Monte Carlo to...

The Branching Random Walk and Contact Process on Galton-Watson and Nonhomogeneous Trees (2001)

Pemantle, Robin, Stacey, Alan M.

We show that the branching random walk on a Galton–Watson tree may have one or two phase transitions, depending on the relative sizes of the mean degree and the maximum degree. We show that there...

A Phase Transition in Random coin Tossing (2001)

Levin, David A., Pemantle, Robin, Peres, Yuval

Suppose that a coin with bias $\theta$ is tossed at renewal times of a renewal process, and a fair coin is tossed at all other times. Let $\mu_\theta$ be the distribution ofthe observed sequence of...

Generating a random sink-free orientation in quadratic time (2001)

Cohn, Henry, Pemantle, Robin, Propp, James

A sink-free orientation of a finite undirected graph is a choice of orientation for each edge such that every vertex has out-degree at least 1. Bubley and Dyer (1997) use Markov Chain Monte Carlo to...

Where Did the Brownian Particle Go? (2001)

Pemantle, Robin; Ohio State University; Pemantle@math.ohio_state.edu, Peres, Yuval; University Of California, Berkeley; Peres@stat.berkeley.edu, Pitman, Jim; University Of California, Berkeley; Pitman@stat.berkeley.edu, Yor, Marc; Université Pierre Et Marie Curie; Pitman@stat.berkeley.edu

Consider the radial projection onto the unit sphere of the path a $d$-dimensional Brownian motion $W$, started at the center of the sphere and run for unit time. Given the occupation measure $mu$ of...

Absence of mutual unbounded growth for almost all parameter values in the two-type Richardson model (2000)

Olle Haggstrom, Robin Pemantle

We study the two-type Richardson model on Z d , d 2, in the asymmetric case where the two particle types have different infection rates. Starting with a single particle of each type, and fixing the...

Theoretical Computer ScienceASYMPTOTICS OF MULTIVARIATE SEQUENCES II. MULTIPLE POINTS OF THE SINGULAR VARIETY. (2000)

Robin Pemantle, Mark C. Wilson, Robin Pemantle, C. Wilson

Abstract. Let F (z) = ∑ r arzr be amultivariate generating function which is meromorphic in some neighborhood of the origin of C d, and let V be its set of singularities. Effective asymptotic...

Vertex-Reinforced Random Walk on Z Has Finite Range (1999)

Pemantle, Robin, Volkov, Stanislav

A stochastic process called vertex-reinforced random walk (VRRW) is defined in Pemantle [Ann. Probab. 16 1229–1241] . We consider this process in the case where the underlying graph is an infinite...

Robust Phase Transitions for Heisenberg and other Models on General Trees (1999)

Pemantle, Robin, Steif, Jeffrey E.

We study several statistical mechanical models on a general tree. Particular attention is devoted to the classical Heisenberg models, where the state space is the $d$-dimensional unit sphere and the...

Asymptotics of multivariate sequences, part I: smooth points of the singular variety (1999)

Robin Pemantle, C. Wilson

r 1 1 z r d d, we determine asymptotics for the coecients. Our approach is to use Cauchy's integral formula near singular points of F, resulting in a tractable oscillating integral. This paper...

Absence of Mutual Unbounded Growth for Almost All Parameter Values in the Two-Type Richardson Model (1999)

Olle Häggström, Robin Pemantle

We study the two-type Richardson model on Z , d 2, in the asymmetric case where the two particle types have different infection rates. Starting with a single particle of each type, and fixing the...

Towards a Theory of Negative Dependence (1999)

Robin Pemantle

: The FKG theorem says that the POSITIVE LATTICE CONDITION, an easily checkable hypothesis which holds for many natural families of events, implies POSITIVE ASSOCIATION, a very useful property. Thus...

Where Did The Brownian Particle Go? (1999)

Robin Pemantle, Yuval Peres, Jim Pitman, Marc Yor

Consider the radial projection onto the unit sphere of the path a d-dimensional Brownian motion W run for unit time. Given the occupation measure ¯ of this projected path, what can be said about the...

Absence of mutual unbounded growth for almost all parameter values in the two-type Richardson model (1999)

Olle Häggström, Robin Pemantle

We study the two-type Richardson model on Z d , d 2, in the asymmetric case where the two particle types have different infection rates. Starting with a single particle of each type, and fixing the...

Vertex-reinforced random walk on Z has finite range (1999)

Robin Pemantle, Stanislav Volkov, Bernard Friedman's Urn

: A stochastic process called Vertex-Reinforced Random Walk (VRRW) is defined in Pemantle (1988a). We consider this process in the case where the underlying graph is an infinite chain (i.e., the...

Robust Phase Transitions for Heisenberg and Other Models on General Trees (1999)

Robin Pemantle, Jeffrey E. Steif

We study several statistical mechanical models on a general tree. Particular attention is devoted to the classical Heisenberg models, where the state space is the d--dimensional unit sphere and the...

Vertex-reinforced random walk on Z has finite range (1999)

Robin Pemantle, Stanislav Volkov, Bernard Friedman's Urn

: A stochastic process called Vertex-Reinforced Random Walk (VRRW) is defined in Pemantle (1988a). We consider this process in the case where the underlying graph is an infinite chain (i.e., the...

Absence of mutual unbounded growth for almost all parameter values in the two-type Richardson model (1999)

Olle Häggström, Robin Pemantle

We study the two-type Richardson model on Z d , d 2, in the asymmetric case where the two particle types have different infection rates. Starting with a single particle of each type, and fixing the...

First passage percolation and a model for competing spatial growth (1998)

Häggström, Olle, Pemantle, Robin

An interacting particle system modelling competing growth on the Z2 lattice is defined as follows. Each x ∈ Z2 is in one of the states {0,1,2}. 1's and 2's remain in their states for ever, while a...

Unpredictable paths and percolation (1998)

Sets avoided by Brownian motion (1998)

4 We construct a nearest-neighbor process ${S_n}$ on Z that is less predictable than simple random walk, in the sense that given the process until time $n$, the conditional probability that $S_{n+k}...

Adelman, Omer, Burdzy, Krzysztof, Pemantle, Robin

A fixed two-dimensional projection of a three-dimensional Brownian motion is almost surely neighborhood recurrent; is this simultaneously true of all the two-dimensional projections with probability...

A Phase Transition in Random Coin Tossing (1998)

David Levin, Robin Pemantle, Yuval Peres

Suppose that a coin with bias ` is tossed at renewal times of a renewal process, and a fair coin is tossed at all other times. Let ` be the distribution of the observed sequence of coin tosses, and...

Moment Conditions for a Sequence With Negative Drift to Be Uniformly Bounded in (1998)

Robin Pemantle, Jeffrey S. Rosenthal

: Suppose a sequence of random variables fX n g has negative drift when above a certain threshold and has increments bounded in L p . When p ? 2 this implies that EX n is bounded above by a constant...

Markov Chains in a Field of Traps (1998)

Robin Pemantle, Stanislav Volkov

: We consider a Markov chain on a countable state space, on which is placed a random field of traps, and ask whether the chain gets trapped almost surely. We show that the quenched problem (when the...

Moment Conditions for a Sequence With Negative Drift to Be Uniformly Bounded in (1998)

Robin Pemantle, Jeffrey S. Rosenthal

: Suppose a sequence of random variables fX n g has negative drift when above a certain threshold and has increments bounded in L p . When p ? 2 this implies that EX n is bounded above by a constant...

to be uniformly bounded in L (1998)

Robin Pemantle, Jeffrey S. Rosenthal

conditions for a sequence with negative drift

No directed fractal percolation in zero area (1997)

Chayes, Lincoln, Pemantle, Robin, Peres, Yuval

We show that fractal (or "Mandelbrot") percolation in two dimensions produces a set containing no directed paths, when the set produced has zero area. This improves a similar result by the first...

Markov chains in a field of traps (1997)

Pemantle, Robin, Volkov, Stanislav

A general criterion is given for when a Markov chain trapped with probability p(x) in state x will be almost surely trapped. The quenched (state x is a trap forever with probability p(x)) and...

Vertex-reinfoced random walk on Z visits finitely many states (1997)

Pemantle, Robin, Volkov, Stanislav

Vertex-reinforced random walk is defined in Pemantle's (1988) thesis; it is a random walk that is biased to visit sites it has already visited a lot. We show that this reinforcement scheme, in...

Sets avoided by Brownian motion (1997)

Adelman, O., Burdzy, Krzysztof, Pemantle, Robin

Any fixed cylinder is hit almost surely by a 3-dimensional Brownian motion, but is there a random cylinder that is in the complement? We answer this for cylinders, and then replacing a cylinder with...

First passage percolation and a model for competing spatial growth (1997)

Haggstrom, Olle, Pemantle, Robin

We generalize Richardson's model by starting with two sites of different colors and giving each new site the color of the site that spawned it. We show that co-existence is possible.

Paths with exponential intersection tails and oriented percolation (1997)

The probability that Brownian motion almost covers a line (1997)

We show that oriented percolation occurs whenever a condition is satisfied called "exponential intersection tails". This condition says that a measure on paths exists for which the probability of two...

The probability that brownian motion almost contains a line (1997)

Lower and upper estimates are given for the probability that the epsilon-enlargement of planar Brownian motion to time 1 (the epsilon sausage) contains a unit line segment. The estimates imply that...

Random walks on the lamplighter group (1996)

Lyons, Russell, Pemantle, Robin, Peres, Yuval

Kaimanovich and Vershik described certain finitely generated groups of exponential growth such that simple random walk on their Cayley graph escapes from the identity at a sublinear rate, or...

Maximum Variation of Total Risk (1996)

Robin Pemantle, Gamma F (t

1 , where fA p t g is the dual previsible projection of the increasing, right-continuous process A t = 1 [Z;1) (t) (see [4]). Examples are when F t is always the trivial oe-field, in which case R = R...

The dimension of the Brownian frontier is greater than 1 (1995)

Bishop, Christopher J., Jones, Peter, Pemantle, Robin, Peres, Yuval

Consider a planar Brownian motion run for finite time. The frontier or ``outer boundary'' of the path is the boundary of the unbounded component of the complement. Burdzy (1989) showed that the...

The Dimension of the Brownian Frontier is Greater Than 1 (1995)

Christopher J. Bishop, Peter W. Jones, Robin Pemantle, Yuval Peres

Consider a planar Brownian motion run for finite time. The frontier or "outer boundary" of the path is the boundary of the unbounded component of the complement. Burdzy (1989) showed that...

Martin Capacity For Markov Chains (1995)

Itai Benjamini, Robin Pemantle, Yuval Peres

The probability that a transient Markov chain, or a Brownian path, will ever visit a given set , is classically estimated using the capacity of with respect to the Green kernel G(x; y). We show that...

The Dimension of the Brownian Frontier is Greater Than 1. (1995)

Christopher J. Bishop, Peter W. Jones, Robin Pemantle, Yuval Peres

Consider a planar Brownian motion run for nite time. The frontier or \outer boundary" of the path is the boundary of the unbounded component of the complement. Burdzy (1989) showed that the...

Diffusion-Limited Aggregation on a Tree (1994)

Martin Barlow, Robin Pemantle, Edwin A. Perkins, U. British, Columbia U. Wisconsin, U. British Columbia

this paper we treat the case ff ! 1; the case ff 1 has already been studied. Our main result, contained in Theorem 6.4 and Corollary 6.5, is as follows

Martin Capacity For Markov Chains And Random Walks In Varying Dimensions (1993)

Itai Benjamini, Robin Pemantle, Yuval Peres

this paper is organized as follows. Martin capacity for Markov chains is the focus of Section 2. Several examples are given, including an interesting relation between simple random walk in three...

When Does a Branching Process Grow Like its Mean? Conceptual Proofs of L log L Criteria (1993)

Russell Lyons, Robin Pemantle, Yuval Peres

. The Kesten-Stigum Theorem is a fundamental criterion for the rate of growth of a supercritical branching process, showing that an L log L condition is decisive. In critical and subcritical cases,...

When Does a Branching Process Grow Like its Mean? Conceptual Proofs of L log L Criteria (1993)

Russell Lyons, Robin Pemantle, Yuval Peres

Abstract. The Kesten-Stigum Theorem is a fundamental criterion for the rate of growth of a supercritical branching process, showing that an L log L condition is decisive. In critical and subcritical...

On Tensor Powers Of Integer Programs (1992)

Robin Pemantle, James Propp, Daniel Ullman

We define a natural product on integer programming problems with nonnegative coefficients. Hypergraph covering problems are a special case of such integer programs, and the product we define is a...

A dynamic model of social network formation

A dynamic model of social network formation

We consider a dynamic social network model in which agents play repeated games in pairings determined by a stochastically evolving social network. Individual agents begin to interact at random, with...

Network formation by reinforcement learning: the long and medium run

We consider a dynamic social network model in which agents play repeated games in pairings determined by a stochastically evolving social network. Individual agents begin to interact at random, with...

Pemantle, Robin, Skyrms, Brian

Learning to Network

Brian Skyrms, Robin Pemantle

Central limit theorem for the size of the range of a renewal process

Hitczenko, Pawel, Pemantle, Robin

We study the range of a Markov chain moving forward on the positive integers. For every position, there is a probability distribution on the size of the next forward jump. Taking a scaling limit as...

Maximum variation of total risk