相关论文: The Poisson boundary of random rational affinities

In this note we study a two-particle bound system (molecule) moving on the positive half-line under the influence of randomly distributed singular two-particle interactions generated by a Poisson process. We give a rigorous definition of…

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 of an adapted random walk on such a group…

We investigate a class of groups acting on possibly exotic affine buildings $X$ and possessing good proximal properties. Such groups are termed of general type, and their dynamics is analyzed through their flag limit sets in the space of…

We study fine structure related to finitely supported random walks on infinite finitely generated discrete groups, largely motivated by dimension group techniques. The unfaithful extreme harmonic functions (defined only on proper space-time…

We generalize the Poisson limit theorem to binary functions of random objects whose law is invariant under the action of an amenable group. Examples include stationary random fields, exchangeable sequences, and exchangeable graphs. A…

In the eighties, A. Connes and E. J. Woods made a connection between hyperfinite von Neumann algebras and Poisson boundaries of time dependent random walks. The present paper explains this connection and gives a detailed proof of two…

In this paper we study a random walk in a one-dimensional dynamic random environment consisting of a collection of independent particles performing simple symmetric random walks in a Poisson equilibrium with density $\rho \in (0,\infty)$.…

We study random walks on groups of isometries of non-proper delta-hyperbolic spaces under the assumption that at least one element in the group satisfies Bestvina-Fujiwara's WPD condition. We show that in this case typical elements are WPD,…

We define matrix groups $FG_n(P)$ for each natural number $n$ and finite set of primes $P$, such that every rational-valued upper triangular matrix group is a (possibly distorted) subgroup. Brofferio and Schapira [Brofferio2011poisson],…

We solve a randomized version of the following open question: is there a strictly convex, bounded curve \gamma in the plane such that the number of rational points on \gamma, with denominator $n$, approaches infinity with $n$? Although this…

Answering a question of Benjamini & Schramm [8], we show that the Poisson boundary of any planar, uniquely absorbing (e.g. one-ended and transient) graph with bounded degrees can be realised geometrically as a circle, namely as the boundary…

Donsker's theorem shows that random walks behave like Brownian motion in an asymptotic sense. This result can be used to approximate expectations associated with the time and location of a random walk when it first crosses a nonlinear…

We identify the Poisson boundary of the dual of the universal compact quantum group A_u(F) with a measurable field of ITPFI factors.

We revisit bosonization of non-relativistic fermions in one space dimension. Our motivation is the recent work on bubbling half-BPS geometries by Lin, Lunin and Maldacena (hep-th/0409174). After reviewing earlier work on exact bosonization…

We show that the problem of Random Walk with boundary attractive potential may be mapped onto the free massive bosonic Quantum Field Theory with a line of defect. This mapping permits to recover the statistical properties of the Random…

In the present paper we find necessary and sufficient conditions for recurrence of random walks on arbitrary subgroups of the group of rational numbers $\mathbb{Q}$.

Interacting particle systems can often be constructed from a graphical representation, by applying local maps at the times of associated Poisson processes. This leads to a natural coupling of systems started in different initial states. We…

We characterize the solutions of the Poisson equation and the domain of its associated one-sided Hilbert transform for Ces\`aro bounded operators of fractional order. The results obtained fairly generalize the corresponding ones for…

The aim of the present work is to show that the results obtained earlier on the approximation of distributions of sums of independent terms by the accompanying compound Poisson laws may be interpreted as rather sharp quantitative estimates…

We study the process of suitably normalized successive return times to rare events in the setting of infinite-measure preserving dynamical systems. Specifically, we consider small neighborhoods of points whose measure tends to zero. We…