Related papers: Random walks in compact groups

Let $\Gamma$ be a countable discrete group, $H$ a lcsc totally disconnected group and $\rho : \Gamma \rightarrow H$ a homomorphism with dense image. We develop a general and explicit technique which provides, for every compact open subgroup…

We establish the (non-lattice) local limit theorem for products of i.i.d. random variables on an arbitrary simply connected nilpotent Lie group $G$, where the variables are allowed to be non-centered. Our result also improves on the known…

Random walks in random scenery are processes defined by $Z_n:=\sum_{k=1}^n\xi_{X_1+...+X_k}$, where $(X_k,k\ge 1)$ and $(\xi_y,y\in\mathbb Z)$ are two independent sequences of i.i.d. random variables. We assume here that their distributions…

We use ideas from topological dynamics (amenability), combinatorics (structural Ramsey theory) and model theory (Fra\" {i}ss\' e limits) to study closed amenable subgroups $G$ of the symmetric group $S_\infty$ of a countable set, where…

It is known that every infinite index quasi-convex subgroup $H$ of a non-elementary hyperbolic group $G$ is a free factor in a larger quasi-convex subgroup of $G$. We give a probabilistic generalization of this result. That is, we show that…

For a finitely generated group G and a banach space X let \alpha^*_X(G) (respectively \alpha^#_X(G)) be the supremum over all \alpha\ge 0 such that there exists a Lipschitz mapping (respectively an equivariant mapping) f:G\to X and c>0 such…

A natural scheme is established for the approximation of quantum Levy processes on locally compact quantum groups by quantum random walks. We work in the somewhat broader context of discrete approximations of completely positive quantum…

It is known that a random walk on $\Z^d$ among i.i.d. uniformly elliptic random bond conductances verifies a central limit theorem. It is also known that approximations of the covariance matrix can be obtained by considering periodic…

Analytic properties of right topological groups have been extensively studied in the compact admissible case (i.e when the group has a dense topological center). This was inspired by the existence of a Haar measure on such groups. In this…

We construct a family of probability measures on the group of Hamiltonian diffeomorphisms of a closed symplectic manifold $(M,\omega)$. We show that these measures are Borel measures with respect to the topology induced by the Hofer metric.…

Let $\nu$ be a probability distribution over the semi-group of square matrices of size $d \ge 2$ over a locally compact field $\mathbb{K}$, \textit{e.g.} $\mathbb{R}$. We consider the random walk $\overline{\gamma}_n :=…

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…

We compute the cone types of the Cayley graph of the modular group $\mathrm{PSL}(2,\mathbf{Z})$ associated with the standard system of generators ${\small\left\{\left(\begin{smallmatrix} 0 & -1 \\ 1 & 0…

The rate of convergence of simple random walk on the Heisenberg group over $Z/nZ$ with a standard generating set was determined by Bump et al [1,2]. We extend this result to random walks on the same groups with an arbitrary minimal…

The paper analyzes a specific class of random walks on quotients of $X:=\text{SL}(k,{\Bbb R})/ \Gamma$ for a lattice $\Gamma$. Consider a one parameter diagonal subgroup, $\{g_t\}$, with an associated abelian expanding horosphere, $U\cong…

We discuss recurrence and ergodicity properties of random walks and associated skew products for large classes of locally compact groups and homogeneous spaces. In particular we show that a closed subgroup of a product of finitely many…

We consider random walks on the torus arising from the action of the group of affine transformations. We give a quantitative equidistribution result for this random walk under the assumption that the Zariski closure of the group generated…

The following question is proposed in [4, Question 1.20]: Let $G$ be a compact group, and suppose that $$\mathcal{N}_k(G) = \{(x1,\dots,x_{k+1}) \in G^{k+1} \;\|; [x_1,\dots, x_{k+1}] = 1\}$$ has positive Haar measure in $G^{k+1}$. Does $G$…

Let $\Gamma$ be a dense subgroup of a simply connected nilpotent Lie group $G$ generated by a finite symmetric set $S$. We consider the $n$-ball $S_n$ for the word metric induced by $S$ on $\Gamma$. We show that $S_n$ (with uniform measure)…

We extend results of Y. Benoist and J.-F. Quint concerning random walks on homogeneous spaces of simple Lie groups to the case where the measure defining the random walk generates a semigroup which is not necessarily Zariski dense, but…