Related papers: Biased random walks on random graphs
Random walks on graphs are widely used in all sciences to describe a great variety of phenomena where dynamical random processes are affected by topology. In recent years, relevant mathematical results have been obtained in this field, and…
This paper studies the on- and off-diagonal upper estimate and the two-sided transition probability estimate of random walks on weighted graphs.
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 propose a model of random walks on weighted graphs where the weights are interval valued, and connect it to reversible imprecise Markov chains. While the theory of imprecise Markov chains is now well established, this is a first attempt…
Lecture notes of a master course given at Orsay between 2019-2024. Topics covered include Part I: One-dimensional random walks, cycle lemma and Bienaym\'e--Galton--Watson random trees. Part II: Erd\"os--R\'enyi random graphs, three proofs…
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.
Random walks on general graphs play an important role in the understanding of the general theory of stochastic processes. Beyond their fundamental interest in probability theory, they arise also as simple models of physical systems. A brief…
Random walks are used for modeling various dynamics in, for example, physical, biological, and social contexts. Furthermore, their characteristics provide us with useful information on the phase transition and critical phenomena of even…
We investigate the directed random walk on hierarchic trees. Two cases are investigated: random variables on deterministic trees with a continuous branching, and random variables on the trees constructed trough the random branching process.…
We study the escape probability problem in random walks over graphs. Given vertices, $s,t,$ and $p$, the problem asks for the probability that a random walk starting at $s$ will hit $t$ before hitting $p$. Such probabilities can be…
We introduce and summarise results from the recent paper 'Biased random walk on the trace of biased random walk on the trace of ...', which was written jointly with M. P. Holmes (University of Melbourne). We also present additional…
We investigate unimodular random networks. Our motivations include their characterization via reversibility of an associated random walk and their similarities to unimodular quasi-transitive graphs. We extend various theorems concerning…
Simple random walks on a partially directed version of $\mathbb{Z}^2$ are considered. More precisely, vertical edges between neighbouring vertices of $\mathbb{Z}^2$ can be traversed in both directions (they are undirected) while horizontal…
We consider random walks in a random environment that is given by i.i.d. Dirichlet distributions at each vertex of Z^d or, equivalently, oriented edge reinforced random walks on Z^d. The parameters of the distribution are a 2d-uplet of…
We present a new approach of topology biased random walks for undirected networks. We focus on a one parameter family of biases and by using a formal analogy with perturbation theory in quantum mechanics we investigate the features of…
Random Walks in Dirichlet Environment (RWDE) correspond to Random Walks in Random Environment (RWRE) on $\Bbb{Z}^d$ where the transition probabilities are i.i.d. at each site with a Dirichlet distribution. Hence, the model is parametrized…
A number of papers have examined various aspects of "random random" walks on finite groups; the purpose of this article is to provide a survey of this work and to show, bring together, and discuss some of the arguments and results in this…
We introduce a class of nearest-neighbor integer random walks in random and non-random media, which includes excited random walks considered in the literature. At each site the random walker has a drift to the right, the strength of which…
We study biased random walks on dynamical percolation in $\mathbb{Z}^d$, which were recently introduced by Andres et al. We provide a second order expansion for the asymptotic speed and show for $d \ge 2$ that the speed of the biased random…
We consider a class of biased random walks on infinite graphs and present several general results on the spectral radius of biased random walk.