Related papers: Poisson boundary for finitely generated groups of …

The group of affine transformations with rational coefficients acts naturally on the real line, but also on the $p$-adic fields. The aim of this note is to show that, for random walks whose laws have a finite first moment, all these actions…

We construct the Poisson boundary for a random walk supported by the general linear group on the rational numbers as the product of flag manifolds over the $p$-adic fields. To this purpose, we prove a law of large numbers using the…

The Poisson boundary of a finite direct product of affine automorphism groups of homogeneous trees is considered. The Poisson boundary is shown to be a product of ends of trees with a hitting measure for spread-out, aperiodic measures of…

The aim of this note is to describe the Poisson boundary of the group of invertible triangular matrices with coefficients in a number field. It generalizes to any dimension and to any number field a result of Brofferio concerning the…

Let $\Gamma$ be a dense countable subgroup of a locally compact continuous group $G$. Take a probability measure $\mu$ on $\Gamma$. There are two natural spaces of harmonic functions: the space of $\mu$-harmonic functions on the countable…

The Poisson boundary of a group G with a probability measure \mu is the space of ergodic components of the time shift in the path space of the associated random walk. Via a generalization of the classical Poisson formula it gives an…

We introduce the discrete affine group of a regular tree as a finitely generated subgroup of the affine group. We describe the Poisson boundary of random walks on it as a space of configurations. We compute isoperimetric profile and Hilbert…

Poisson boundary is a measurable $\Gamma$-space canonically associated with a group $\Gamma$ and a probability measure $\mu$ on it. The collection of all measurable $\Gamma$-equivariant quotients, known as $\mu$-boundaries, of the Poisson…

We give a geometric description of the Poisson boundaries of certain extensions of free and hyperbolic groups. In particular, we get a full description of the Poisson boundaries of free-by-cyclic groups. We rely upon the description of…

For any countable group with infinite conjugacy classes we construct a family of forests on the group. For each of them there is a random walk on the group with the property that its sample paths almost surely converge to the geometric…

For a locally compact quantum group $\mathbb{G}$, consider the convolution action of a quantum probability measure $\mu$ on $L_\infty(\mathbb{G})$. As shown by Junge--Neufang--Ruan, this action has a natural extension to a Markov map on…

We prove that random walks on Thompson's group $F$ driven by strictly non-degenerate finitely supported probability measures $\mu$ have a non-trivial Poisson boundary. The proof consists in an explicit construction of two different…

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

Given a finitely generated group, the well-known Stability Problem asks whether the non-triviality of the Poisson-Furstenberg boundary (which is equivalent to the existence of non-constant bounded harmonic functions) depends on the choice…

Let T be the homogeneous tree with degree and G a finitely generated group whose Cayley graph is T. The associated lamplighter group is the wreath product of the cyclic group of order r with G. For a large class of random walks on this…

We consider a finite-dimensional, locally finite CAT(0) cube complex X admitting a co-compact properly discontinuous countable group of automorphisms G. We construct a natural compact metric space B(X) on which G acts by homeomorphisms, the…

We prove that for any non-trivial product-type action of SUq(n) (0<q<1) on an ITPFI factor N, the relative commutant of the fixed point algebra in N is isomorphic to the algebra of bounded measurable functions on the quantum flag manifold.…

We show that a Poisson Lie group $(G,\pi)$ is coboundary if and only if the natural action of $G\times G$ on $M=G$ is a Poisson action for an appropriate Poisson structure on $M$ (the structure turns out to be the well known $\pi _+$). We…

We compute the Poisson boundary of locally discrete groups of diffeomorphisms of the circle.

Consider a finite l-group acting on the affine space of dimension n over a field k, whose characteristic differs from l. We prove the existence of a fixed point, rational over k, in the following cases: --- The field k is p-special for some…