Related papers: Random walks in a random environment
Central limit theorems for random walks in quenched random environments have attracted plenty of attention in the past years. More recently still, finer local limit theorems -- yielding a Gaussian density multiplied by a highly oscillatory…
In this note, we try to analyze and clarify the intriguing interplay between some counting problems related to specific thermalized weighted graphs and random walks consistent with such graphs.
This paper considers 1-dimensional generalized random walks in random scenery. That is, the steps of the walk are generated by an arbitrary stationary process, and also the scenery is a priori arbitrary stationary. Under an ergodicity…
Many important transport phenomena are described by simple mathematical models rooted in the diffusion equation. Geometrical constraints present in such phenomena often have influence of a universal sort and manifest themselves in scaling…
We consider discrete-time nearest-neighbor quantum walks on random environments in one dimension. Using the method based on a path counting, we present both quenched and annealed weak limit theorems for the quantum walk.
Random Walk is a basic algorithm to explore the structure of networks, which can be used in many tasks, such as local community detection and network embedding. Existing random walk methods are based on single networks that contain limited…
The behavior of the maximal displacement of a supercritical branching random walk has been a subject of intense studies for a long time. But only recently the case of time-inhomogeneous branching has gained focus. The contribution of this…
This tutorial article showcases the many varieties and uses of quantum walks. Discrete time quantum walks are introduced as counterparts of classical random walks. The emphasis is on the connections and differences between the two types of…
Recently, quantized versions of random walks have been explored as effective elements for quantum algorithms. In the simplest case of one dimension, the theory has remained divided into the discrete-time quantum walk and the continuous-time…
In this paper we introduce the notion of Random Walk in Changing Environment - a random walk in which each step is performed in a different graph on the same set of vertices, or more generally, a weighted random walk on the same vertex and…
We prove results for random walks in dynamic random environments which do not require the strong uniform mixing assumptions present in the literature. We focus on the "environment seen from the walker"-process and in particular its…
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…
Issues of resonance that appear in non-standard random walk models are discussed. The first walk is called repulsive delayed random walk, which is described in the context of a stick balancing experiment. It will be shown that a type of…
We consider a random walk in an i.i.d. random environment on Z that is perturbed by cookies of strength 1. The number of cookies per site is assumed to be i.i.d. Results on the speed of the random walk are obtained. Our main tool is the…
This paper works out the rate of convergence of two "natural" random walks on the dicyclic group.
We study the properties of discrete-time random walks on networks formed by randomly interconnected cliques, namely, random networks of cliques. Our purpose is to derive the parameters that define the network structure -- specifically, the…
Random walk on the set of irreducible representations of a finite group is investigated. For the symmetric and general linear groups, a sharp convergence rate bound is obtained and a cutoff phenomenon is proved. As related results, an…
We consider the general branching random walk under minimal assumptions, which in particular guarantee that the empirical particle distribution admits an almost sure central limit theorem. For such a process, we study the large time decay…
We consider a discrete random walk on a diagonal lattice in two and three dimensions and obtain explicit solutions of absorption probabilities and probabilities of return in several domains. In three dimensions we consider both the cube and…
We consider a model of random walk in ${\mathbb Z}^2$ with (fixed or random) orientation of the horizontal lines (layers) and with non constant iid probability to stay on these lines. We prove the transience of the walk for any fixed…