Related papers: Sign-time distribution for a random walker with a …
We study a discrete-time random walk on the non-negative integers, such that when 0 is reached a jump occurs to an arbitrary location, with given probabilities. We obtain an asymptotic formula for the expected position at large times, in…
We analyse the mixing profile of a random walk on a dynamic random permutation, focusing on the regime where the walk evolves much faster than the permutation. Two types of dynamics generated by random transpositions are considered: one…
Random walks, and in particular, their first passage times, are ubiquitous in nature. Using direct enumeration of paths, we find the first return time distribution of a 1D random walker, which is a heavy-tailed distribution with infinite…
We consider a continuous-time random walk which is the generalization, by means of the introduction of waiting periods on sites, of the one-dimensional nonhomogeneous random walk with a position-dependent drift known in the mathematical…
In this paper we present a computation of the mean first-passage times both for a random walk in a discrete bounded lattice, between a starting site and a target site, and for a Brownian motion in a bounded domain, where the target is a…
The aim of this paper is to represent any continuous local martingale as an almost sure limit of a nested sequence of simple, symmetric random walks, time changed by a discrete quadratic variation process. One basis of this is a similar…
Consider an arbitrary transient random walk on $\Z^d$ with $d\in\N$. Pick $\alpha\in[0,\infty)$ and let $L_n(\alpha)$ be the spatial sum of the $\alpha$-th power of the $n$-step local times of the walk. Hence, $L_n(0)$ is the range,…
The position density of a "particle" performing a continuous-time quantum walk on the integer lattice, viewed on length scales inversely proportional to the time t, converges (as t tends to infinity) to a probability distribution that…
There is a long history of establishing central limit theorems for Markov chains. Quantitative bounds for chains with a spectral gap were proved by Mann and refined later. Recently, rates of convergence for the total variation distance were…
We propose an analytical method to determine the shape of density profiles in the asymptotic long time limit for a broad class of coupled continuous time random walks which operate in the ballistic regime. In particular, we show that…
We study a scenario under which variable step random walks give anomalous statistics. We begin by analyzing the Martingale Central Limit Theorem to find a sufficient condition for the limit distribution to be non-Gaussian. We note that the…
One-parameter family of discrete-time quantum-walk models on the square lattice, which includes the Grover-walk model as a special case, is analytically studied. Convergence in the long-time limit $t \to \infty$ of all joint moments of two…
We study the time evolution of continuous-time quantum walks on randomly changing graphs. At certain moments edges of the graph appear or disappear with a given probability. We focus on the case when the time interval between subsequent…
Consider a random walk $S_n=\sum_{i=0}^n X_i$ with negative drift. This paper deals with upper bounds for the maximum $M=\max_{n\ge 1}S_n$ of this random walk in different settings of power moment existences. As it is usual for deriving…
We formulate the generalized master equation for a class of continuous time random walks in the presence of a prescribed deterministic evolution between successive transitions. This formulation is exemplified by means of an…
We study the asymptotic behavior of zero-drift random walks confined to multidimensional convex cones, when the endpoint is close to the boundary. We derive a local limit theorem in the fluctuation regime.
We study the probability distribution, $P_N(T)$, of the coincidence time $T$, i.e. the total local time of all pairwise coincidences of $N$ independent Brownian walkers. We consider in details two geometries: Brownian motions all starting…
We study the distributions of the continuous-time quantum walk on a one-dimensional lattice. In particular we will consider walks on unbounded lattices, walks with one and two boundaries and Dirichlet boundary conditions, and walks with…
We obtain the exact asymptotic result for the disorder-averaged probability distribution function for a random walk in a biased Sinai model and show that it is characterized by a creeping behavior of the displacement moments with time,…
We studied simple random-walk models with asymmetric time delays. Stochastic simulations were performed for hyperbolic-tangent fitness functions and to obtain analytical results we approximated them by step functions. A novel behavior has…