相关论文: Returns to origin of a one-dimensional random walk…
A cyclic random walk is a random walk whose transition probabilities/rates can be written as a superposition of the empirical measures of a family of finite cycles. This identifies a convex set of models. We discuss the problem of…
We consider random paths on a square lattice which take a left or a right turn at every vertex. The possible turns are taken with equal probability, except at a vertex which has been visited before. In such case the vertex is left via the…
A certain class of directed metric graphs is considered. Asymptotics for a number of possible endpoints of a random walk at large times is found.
Benjamini,Haggstrom, Peres and Steif introduced the model of dynamical random walk on Z^d. This is a continuum of random walks indexed by a parameter t. They proved that for d=3,4 there almost surely exist t such that the random walk at…
We show that the "twisted" planar random walk - which results by summing up stationary increments rotated by multiples of a fixed angle - is recurrent under diverse assumptions on the increment process. For example, if the increment process…
We study a random walk on $\mathbb{Z}$ which evolves in a dynamic environment determined by its own trajectory. Sites flip back and forth between two modes, $p$ and $q$. $R$ consecutive right jumps from a site in the $q$-mode are required…
A proof is provided of a strong law of large numbers for a one-dimensional random walk in a dynamic random environment given by a supercritical contact process in equilibrium. The proof is based on a coupling argument that traces the…
The asymptotic mean number of distinct sites visited by a subdiffusive continuous time random walker in two dimensions seems not to have been explicitly calculated anywhere in the literature. This number has been calculated for other…
We study the problem of site recurrence of discrete time nearest neighbor open quantum random walks (OQWs) on the integer line, proving basic properties and some of its relations with the corresponding problem for unitary (coined) quantum…
Random walks as well as diffusions in random media are considered. Methods are developed that allow one to establish large deviation results for both the `quenched' and the `averaged' case.
We consider several variants of a class of random walks whose increment distributions depend on the average value of the process over its most recent $N$ steps. We investigate the speed of the process, and in particular, the limiting speed…
When it comes to random walk on the integers $\mathbb{Z}$, the arguably first step of generalization beyond simple random walk is the class of one-sidedly continuous random walk, where the stepsize in only one direction is bounded by 1.…
In rotor walk on a finite directed graph, the exits from each vertex follow a prescribed periodic sequence. Here we consider the case of rotor walk where a particle starts from a designated source vertex and continues until it hits a…
In this paper, we study the scaling limit of a class of random walks which behave like simple random walks outside of a bounded region around the origin and which are subject to a partial reflection near the origin. If the probability of…
The quantum walk is a counterpart of the random walk. The 2-state quantum walk in one dimension can be determined by a measure on the unit circle in the complex plane. As for the singular continuous measure, results on the corresponding…
We present numerical study of a model of quantum walk in periodic potential on the line. We take the simple view that different potentials affect differently the way the coin state of the walker is changed. For simplicity and definiteness,…
We study a random walk in random environment on the non-negative integers. The random environment is not homogeneous in law, but is a mixture of two kinds of site, one in asymptotically vanishing proportion. The two kinds of site are (i)…
We consider random walks in the form of nearest-neighbor hopping on Erdos-Renyi random graphs of finite fixed mean degree c as the number of vertices N tends to infinity. In this regime, using statistical field theory methods, we develop an…
We study exploration properties of a random walk on a network. For a fully connected network we find that the problem can be mapped to the well known coupon collector problem, thus allowing us to estimate form of $P(S,t)$: the distribution…
A survey is presented of known results concerning simple random walk on the class of distance-regular graphs. One of the highlights is that electric resistance and hitting times between points can be explicitly calculated and given strong…