Related papers: Simple random walk on distance-regular graphs
We consider transient nearest neighbor random walks on the positive part of the real line. We give criteria for the finiteness of the number of cutpoints and strong cutpoints. Examples and open problems are presented.
Random graphs with a given degree sequence are often constructed using the configuration model, which yields a random multigraph. We may adjust this multigraph by a sequence of switchings, eventually yielding a simple graph. We show that,…
Focusing on coupling between edges, we generalize the relationship between the normalized graph Laplacian and random walks on graphs by devising an appropriate normalization for the Hodge Laplacian -- the generalization of the graph…
Previous work has shown the effectiveness of random walk hitting times as a measure of dissimilarity in a variety of graph-based learning problems such as collaborative filtering, query suggestion or finding paraphrases. However,…
This paper is about the construction of displacement interpolations on a discrete metric graph. Our approach is based on the approximation of any optimal transport problem whose cost function is a distance on a discrete graph by a sequence…
The usual random walk on a group (homogeneous both in time and in space) is determined by a probability measure on the group. In a random walk with random transition probabilities this single measure is replaced with a stationary sequence…
This article introduces a model for interacting vertex-reinforced random walks, each taking values on a complete sub-graph of a locally finite undirected graph. The transition probability for a walk to a given vertex depends on the…
We show that on every Ramanujan graph $G$, the simple random walk exhibits cutoff: when $G$ has $n$ vertices and degree $d$, the total-variation distance of the walk from the uniform distribution at time $t=\frac{d}{d-2}\log_{d-1} n +…
We construct a renewal structure for random walks on surface groups. The renewal times are defined as times when the random walks enters a particular type of a cone and never leaves it again. As a consequence, the trajectory of the random…
We consider an analogue of the Kac random walk on the special orthogonal group $SO(N)$, in which at each step a random rotation is performed in a randomly chosen 2-plane of $\bR^N$. We obtain sharp asymptotics for the rate of convergence in…
We give refined estimates for the discrete time and continuous time versions of some basic random walks on the symmetric and alternating groups $S_n$ and $A_n$. We consider the following models: random transposition, transpose top with…
We consider a class of self-interacting random walks in deterministic or random environments, known as excited random walks or cookie walks, on the d-dimensional integer lattice. The main purpose of this paper is two-fold: to give a survey…
It is a common practice to describe branching random walks in terms of birth, death and walk of particles, which makes it easier to use them in different applications. The main results obtained for the models of symmetric continuous-time…
We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices $x$ and $y$ are connected with probability that asymptotically behaves like $|x-y|^{-\alpha}$ with $\alpha>d$,…
In the present paper, we give the exact formula for the average hitting time (HT, as an abbreviation) of random walks from one vertex to any other vertex on the some weighted Cayley graphs.
Random walks on regular bounded degree expander graphs have numerous applications. A key property of these walks is that they converge rapidly to the uniform distribution on the vertices. The recent study of expansion of high dimensional…
The range, local times, and periodicity of symmetric, weakly asymmetric and asymmetric random walks at the time of exit from a strip with $N$ locations are considered. Several results on asymptotic distributions are obtained.
We consider a dynamic random graph on $n$ vertices that is obtained by starting from a random graph generated according to the configuration model with a prescribed degree sequence and at each unit of time randomly rewiring a fraction…
An analytic effective medium theory is constructed to study the mean access times for random walks on hybrid disordered structures formed by embedding complex networks into regular lattices, considering transition rates $F$ that are…
Distance-regular graphs have many beautiful combinatorial properties. Distance-transitive graphs have very strong symmetries, and they are distance-regular, i.e. distance-transitivity implies distance-regularity. In this paper, we give…