The Poincaré Series Of C\Z (2007)
. We show that the Poincar'e series of the Fuchsian group of deck transformations of C nZdiverges logarithmically. This is because C nZis a Z-cover of the three horned sphere, whence its...
. We prove local limit theorems for Gibbs-Markov processes in the domain of attraction of normal distributions. x1 Introduction It is well known that a random variable X belongs to the domain of...
We prove local limit theorems for Gibbs-Markov processes in the domain of attraction of normal distributions.
Predictability, entropy and information of infinite transformations (2007)
Aaronson, Jon, Park, Kyewon Koh
We show that a certain type of quasi finite, conservative, ergodic, measure preserving transformation always has a maximal zero entropy factor, generated by predictable sets. We also construct a...
L{infty} Eigenvalues and L2 Spectra of Non-Singular Transformations (2006)
Aaronson, Jon, Nadkarni, Mahendra
There is a natural interplay between the L∞ eigenvalue group of a non-singular transformation and its L2 spectra via systems of imprimitivity. This aids us, on the one hand, to compute some new...
The Visitors to Zero of Some Deterministic Random Walks (2006)
We study the asymptotic behaviour of the functions $${\Psi }_{n}\left(x\right)=\left\{1\le k\le n:{\phi }_{k}\left(x\right)=0\right\}$$ where $${\varphi }_{n}\left(x\right)={\sum }_{k=0}^{n-1}\phi...
Absolutely continuous, invariant measures for dissipative, ergodic transformations (2005)
Aaronson, Jon., Meyerovitch, Tom
We show that a dissipative, ergodic measure preserving transformation of a sigma-finite, non-atomic measure space always has many non-proportional, absolutely continuous, invariant measures and is...
Exchangeable, Gibbs and equilibrium measures for Markov subshifts (2005)
Aaronson, Jon., Nakada, Hitoshi
We study a class of strongly irreducible, multidimensional, topological Markov shifts, comparing two notions of "symmetric measure": exchangeability and the Gibbs (or conformal) property. We show...
Exactness of Rokhlin endomorphisms and weak mixing of Poisson boundaries (2004)
Aaronson, Jon, Lemanczyk, Mariusz
We give conditions for the exactness of Rokhlin endomorphisms, apply these to random walks on locally compact, second countable topological groups and obtain that the action on the Poisson boundary...
On the mixing coefficients of piecewise monotonic maps (2004)
Aaronson, Jon, Nakada, Hitoshi
We investigate the mixing coefficients of interval maps satisfying Rychlik's conditions. A mixing Lasota-Yorke map is reverse $\phi$-mixing. If its invariant density is uniformly bounded away from 0,...
Aaronson, Jon., Lemanczyk, Mariusz, Volny, Dalibor
We study the centraliser of locally compact group extensions of ergodic probability preserving transformations. New methods establishing ergodicity of group extensions are introduced, and new...
Occupation times of sets of infinite measure for ergodic transformations (2004)
Aaronson, Jon, Thaler, Maximilian, Zweimueller, Roland
Assume that $T$ is a conservative ergodic measure preserving transformation of the infinite measure space $(X,\mathcal{A},\mu)$.We study the asymptotic behaviour of occupation times of certain...
Group Extensions Of Gibbs-Markov Maps (1999)
. Let be an aperiodic cocycles with values in a locally compact abelian second countable group G dened on an exact Gibbs-Markov map T : X ! X. We show that the group extension T (x; g) = (T (x); g +...
Exact Group Extensions Of Markov Maps. (1999)
. We give conditions for the exactness of R d -extensions of Markov maps. x0 Introduction A nonsingular transformation (X; B; m;T ) of a standard probability space is called a Markov map if there is...
Characteristic functions of random variables attracted to $1$-stable laws (1998)
Aaronson, Jon, Denker, Manfred
The domain of attraction of a 1-stable law on $\mathbf{R}^d$ is characterized by the expansions of the characteristic functions of its elements.
Characteristic Functions Of Random Variables Attracted To 1-Stable Laws (1995)
Jon. Aaronson, Manfred Denker, Where An R, Bn Are Constants
. The domain of attraction of a 1-stable law on R d is characterised by the expansions of the characteristic functions of its elements. x0 introduction Let X 1 ; X 2 ; : : : be R d -valued,...
Local Limit Theorems For Gibbs-Markov Maps
. We prove conditional local limit theorems for Gibbs-Markov processes whose marginals are in the domain of attraction of a stable law with order in (0; 2). c fl1996. Introduction Given a R-valued...