Related papers: Random walks of infinite moment on free semigroups

A classical construction associates to a transient random walk on a discrete group $\Gamma$ a compact $\Gamma$-space $\partial_M \Gamma$ known as the Martin boundary. The resulting crossed product $C^*$-algebra $C(\partial_M \Gamma)…

Random walks on a group $G$ model many natural phenomena. A random walk is defined by a probability measure $p$ on $G$. We are interested in asymptotic properties of the random walks and in particular in the linear drift and the asymptotic…

In this paper we continue our study of a multidimensional random walk with zero mean and finite variance killed on leaving a cone. We suggest a new approach that allows one to construct a positive harmonic function in Lipschitz cones under…

We consider a group G of isometries acting on a (not necessarily geodesic) delta-hyperbolic space X and possessing a radial limit set of full measure within its limit set. For any continuous quasiconformal measure w supported on the limit…

Let $G$ be a real Lie group, $\Lambda\leq G$ a lattice, and $\Omega=G/\Lambda$. We study the equidistribution properties of the left random walk on $\Omega$ induced by a probability measure $\mu$ on $G$. It is assumed that $\mu$ has a…

Let $G$ be a connected semisimple real Lie group with finite center, and $\mu$ a probability measure on $G$ whose support generates a Zariski-dense subgroup of $G$. We consider the right $\mu$-random walk on $G$ and show that each random…

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 prove sharp limit theorems on random walks on graphs with values in finite groups. We then apply these results (together with some elementary algebraic geometry, number theory, and representation theory) to finite quotients of lattices…

We begin by giving a new proof of the equivalence between the Liouville property and vanishing of the drift for symmetric random walks with finite first moments on finitely generated groups; a result which was first established by…

In this paper we introduce for a group $G$ the notion of ultralimit of measure class preserving actions of it, and show that its Furstenberg-Poisson boundaries can be obtained as an ultralimit of actions on itself, when equipped with…

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…

Consider a sequence of independent random isometries of Euclidean space with a previously fixed probability law. Apply these isometries successively to the origin and consider the sequence of random points that we obtain this way. We prove…

Let $\mu$ be a probability measure on $\text{Out}(F_N)$ with finite first logarithmic moment with respect to the word metric, finite entropy, and whose support generates a nonelementary subgroup of $\text{Out}(F_N)$. We show that almost…

We define an electrification of the curve graph of a surface S of finite type and use it to identify the Poisson boundary of a random walk on the mapping class group of S with some logarithmic moment condition as a stationary measure on the…

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 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,…

Using coordinate-free basic operators on toy Fock spaces \cite{AP}, quantum random walks are defined following the ideas in \cite{LP,AP}. Strong convergence of quantum random walks associated with bounded structure maps is proved under…

We describe a new construction of a family of measures on a group with the same Poisson boundary. Our approach is based on applying Markov stopping times to an extension of the original random walk.

The concept of a random walk on a finite group converging to random - and a way of measuring the distance to random after $k$ transitions - is generalised from the classical case to the case of random walks on finite quantum groups. A…

We introduce a family of atomic measures on free groups generated by no-return random walks. These measures are shown to be very convenient for comparing "relative sizes" of subgroups, context-free and regular subsets (that, subsets…