Related papers: Random walks on free products of cyclic groups

We show bounds on total variation and $L^{\infty}$ mixing times, spectral gap and magnitudes of the complex valued eigenvalues of a general (non-reversible non-lazy) Markov chain with a minor expansion property. This leads to the first…

We prove the existence and uniqueness of a discrete nonnegative harmonic function for a random walk satisfying finite range, centering and ellipticity conditions, killed when leaving a globally Lipschitz domain in $\mathbb{Z}^d$. Our method…

Let $G$ be a finitely generated group and $X$ its Cayley graph with respect to a finite, symmetric generating set $S$. Furthermore, let $H$ be a finite group and $H \wr G$ the lamplighter group (wreath product) over $G$ with group of…

We study an irreducible Markov chain on the category of finite abelian $p$-groups, whose stationary measure is the Cohen-Lenstra distribution. This Markov chain arises when one studies the cokernel of a random matrix $M$, after conditioning…

In this paper we study asymptotic properties of symmetric and non-degenerate random walks on transient hyperbolic groups. We prove a central limit theorem and a law of iterated logarithm for the drift of a random walk, extending previous…

Random walk on changing graphs is considered. For sequences of finite graphs increasing monotonically towards a limiting infinite graph, we establish transition probability upper bounds. It yields sufficient transience criteria for simple…

On a finite graph, there is a natural family of Boltzmann probability measures on cycle-rooted spanning forests, parametrized by weights on cycles. For a certain subclass of those weights, we construct Gibbs measures in infinite volume, as…

Let $\Gamma$ be a countable group acting on a geodesic Gromov-hyperbolic metric space $X$ and $\mu$ a probability measure on $\Gamma$ whose support generates a non-elementary subsemigroup. Under the assumption that $\mu$ has a finite…

We introduce and study a class of random walks on lamplighter groups $H\wr G$, where $H$ is a nontrivial finitely generated group and $G$ is an infinite finitely generated group, called \textbf{stationary random walks}. At each step, the…

Given a probability measure on a finitely generated group, its Martin boundary is a natural way to compactify the group using the Green function of the corresponding random walk. For finitely supported measures in hyperbolic groups, it is…

We study models of continuous time, symmetric, $\Z^d$-valued random walks in random environments. One of our aims is to derive estimates on the decay of transition probabilities in a case where a uniform ellipticity assumption is absent. We…

We consider nondegenerate, finitely supported random walks on a finitely generated Gromov hyperbolic group. We show that the entropy and the escape rate are Lipschitz functions of the probability if the support remains constant.

Initial steps are presented towards understanding which finitely generated groups are almost surely generated as semigroups by the path of a random walk on the group.

We analyze random walks on a class of semigroups called ``left-regular bands''. These walks include the hyperplane chamber walks of Bidigare, Hanlon, and Rockmore. Using methods of ring theory, we show that the transition matrices are…

Let $\Gamma$ act on a countable set V with only finitely many orbits. Given a $\Gamma$-invariant random environment for a Markov chain on V and a random scenery, we exhibit, under certain conditions, an equivalent stationary measure for the…

In this paper we present the construction of explicit quasi-isomorphisms that compute the cyclic homology and periodic cyclic homology of crossed-product algebras associated with (discrete) group actions. In the first part we deal with…

We consider non-degenerate, finitely supported random walks on a free group. We show that the entropy and the linear drift vary analytically with th eprobability of constant support.

In this paper, we study properties of random walks on finite groups and later use them to obtain the limiting braid length expectation and component number of braid closure in a model of random braids, which is constructed by lifting…

A one-dimensional confined Nonlinear Random Walk is a tuple of $N$ diffeomorphisms of the unit interval driven by a probabilistic Markov chain. For generic such walks, we obtain a geometric characterization of their ergodic stationary…

We consider the simple random walk on the infinite cluster of a general class of percolation models on $\mathbb{Z}^d$, $d\geq 3$, including Bernoulli percolation as well as models with strong, algebraically decaying correlations. For almost…