Related papers: On laws of large numbers for random walks

We establish a strong law of large numbers for one-dimensional continuous-time random walks in dynamic random environments under two main assumptions: the environment is required to satisfy a decoupling inequality that can be interpreted as…

We prove that in any recurrent reversible random rooted graph, two independent simple random walks started at the same vertex collide infinitely often almost surely. This applies to the Uniform Infinite Planar Triangulation and…

We study random walks on sub-Riemannian manifolds using the framework of retractions, i.e., approximations of normal geodesics. We show that such walks converge to the correct horizontal Brownian motion if normal geodesics are approximated…

Consider p independent Brownian motions in R^d, each running up to its first exit time from an open domain B, and their intersection local time l as a measure on B. We give a sharp criterion for the finiteness of exponential moments,…

Let $G$ be a connected simple real Lie group, $\Lambda_{0}\subseteq G$ a lattice and $\Lambda \unlhd \Lambda_{0}$ a normal subgroup such that $\Lambda_{0}/\Lambda\simeq \mathbb{Z}^d$. We study the drift of a random walk on the…

Following the recent work of Sznitman (arXiv:0805.4516), we investigate the microscopic picture induced by a random walk trajectory on a cylinder of the form G_N x Z, where G_N is a large finite connected weighted graph, and relate it to…

For an arbitrary transient random walk $(S_n)_{n\ge 0}$ in $\mathbb Z^d$, $d\ge 1$, we prove a strong law of large numbers for the spatial sum $\sum_{x\in\mathbb Z^d}f(l(n,x))$ of a function $f$ of the local times…

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 study time-inhomogeneous random walks on finite groups in the case where each random walk step need not be supported on a generating set of the group. When the supports of the random walk steps satisfy a natural condition involving…

We provide a direct proof of Cram\'er's theorem for geodesic random walks in a complete Riemannian manifold $(M,g)$. We show how to exploit the vector space structure of the tangent spaces to study large deviation properties of geodesic…

In this brief note, we study the strong law of large numbers for random walks in random scenery. Under the assumptions that the random scenery is non-stationary and satisfies weakly dependent condition with an appropriate rate, we establish…

In this note, we give an original convergence result for products of independent random elements of motion group. Then we consider dynamic random walks which are inhomogeneous Markov chains whose transition probability of each step is, in…

We consider (random) walks in a multidimensional orthant. Using the idea of universality in probability theory, one can associate a unique polyhedral domain to any given walk model. We use this connection to prove two sets of new results.…

We study the asymptotic behavior of a multidimensional random walk in a general cone. We find the tail asymptotics for the exit time and prove integral and local limit theorems for a random walk conditioned to stay in a cone. The main step…

Edgeworth expansions for random walks on covering graphs with groups of polynomial volume growths are obtained under a few natural assumptions. The coefficients appearing in this expansion depends on not only geometric features of the…

We study the asymptotic behavior of the simple random walk on oriented versions of $\mathbb{Z}^2$. The considered lattices are not directed on the vertical axis but unidirectional on the horizontal one, with random orientations whose…

We propose a general framework for quantum walks on d-dimensional spaces. We investigate asymptotic behavior of these walks. Among them, existence of limit distribution of homogeneous walks is proved. In this theorem, the support of the…

We examine the question of whether a collection of random walks on a graph can be coupled so that they never collide. In particular, we show that on the complete graph on n vertices, with or without loops, there is a Markovian coupling…

In this paper we study random walks on dynamical random environments in $1 + 1$ dimensions. Assuming that the environment is invariant under space-time shifts and fulfills a mild mixing hypothesis, we establish a law of large numbers and a…

We prove strong theorems for the local time at infinity of a nearest neighbor transient random walk. First, laws of the iterated logarithm are given for the large values of the local time. Then we investigate the length of intervals over…