Related papers: Cutoff for random walks on dihedral groups
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…
In the present paper we find necessary and sufficient conditions for recurrence of random walks on arbitrary subgroups of the group of rational numbers $\mathbb{Q}$.
The main aim of the present set of notes is to give new, short and essentially self-contained proofs of some classical, as well as more recent, results about random walks on groups. For instance, we shall see that the drift characterization…
In this paper, we study discrete-time quantum walks on one-dimensional lattices. We find that the coherent dynamics depends on the initial states and coin parameters. For infinite size of lattice, we derive an explicit expression for the…
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 bound the rate of convergence to uniformity for certain random walks on the complete monomial groups G \wr S_n for any group G. These results provide rates of convergence for random walks on a number of groups of interest: the…
We show that the total-variation mixing time of the lamplighter random walk on fractal graphs exhibit sharp cutoff when the underlying graph is transient (namely of spectral dimension greater than two). In contrast, we show that such cutoff…
This paper is concerned with random walks on a family of dyadic-valued solvable matrix groups. A description of the Poisson boundary of these groups for probability measures of finite first moment and non-zero displacements (or drifts) is…
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…
We define matrix groups $FG_n(P)$ for each natural number $n$ and finite set of primes $P$, such that every rational-valued upper triangular matrix group is a (possibly distorted) subgroup. Brofferio and Schapira [Brofferio2011poisson],…
Exact coupling of random walks is studied. Conditions for admitting a successful exact coupling are given that are necessary and in the Abelian case also sufficient. In the Abelian case, it is shown that a random walk $S$ with step-length…
We study random walks on groups with the feature that, roughly speaking, successive positions of the walk tend to be "aligned". We formalize and quantify this property by means of the notion of deviation inequalities. We show that deviation…
We construct a family of trees on which a lazy simple random walk exhibits total variation cutoff. The main idea behind the construction is that hitting times of large sets should be concentrated around their means. For this sequence of…
We show that a sequence of birth-and-death chains, given by lazy random walks in a (transient) environment (RWRE) on [0; n], exhibits a cutoff in the ballistic regime but does not exhibit a cutoff in the (interior of) the subballistic…
Let $G$ be a real Lie group, $\Lambda\leq G$ a lattice, and $\Omega=G/\Lambda$. We study the equidistribution properties of the left random walk on $\Omega$ induced by a probability measure $\mu$ on $G$. It is assumed that $\mu$ has a…
Interactive programming environments are powerful tools for promoting innovative network thinking, teaching science of complexity, and exploring emergent phenomena. This paper reports on our recent development of the deterministic random…
We identify a relationship between a certain family of random walks on Euclidean lattices and difference matrices over cyclic groups. We then use the techniques of Fourier analysis to estimate the return probabilities of these random walks,…
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…
This article investigates the behavior of the continuous-time simple random walk on $\mathbb{Z}^d$, $d \geq 3$. We derive an asymptotic lower bound on the principal exponential rate of decay for the probability that the average value over a…
We pose a new and intriguing question motivated by distributed computing regarding random walks on graphs: How long does it take for several independent random walks, starting from the same vertex, to cover an entire graph? We study the…