Related papers: First-passage times for random walks in the triang…

In this article, we study a branching random walk in an environment which depends on the time. This time-inhomogeneous environment consists of a sequence of macroscopic time intervals, in each of which the law of reproduction remains…

We study the asymptotic tail probability of the first-passage time over a moving boundary for a random walk conditioned to return to zero, where the increments of the random walk have finite variance. Typically, the asymptotic tail behavior…

We investigate the distribution of the time spent by a random walker to the right of a boundary moving with constant velocity v. For the continuous-time problem (Brownian motion), we provide a simple alternative proof of Newman's recent…

This article rigorously analyzes the meeting time between pursuers and evaders performing random walks on digraphs. There exist several bounds on the expected meeting time between random walkers on graphs in the literature, however,…

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 derive a perturbation expansion for general self-interacting random walks, where steps are made on the basis of the history of the path. Examples of models where this expansion applies are reinforced random walk, excited random walk, the…

In this paper, we investigate random walks in a family of small-world trees having an exponential degree distribution. First, we address a trapping problem, that is, a particular case of random walks with an immobile trap located at the…

We identify a fundamental phenomenon of heterogeneous one dimensional random walks: the escape (traversal) time is maximized when the heterogeneity in transition probabilities forms a pyramid-like potential barrier. This barrier corresponds…

For random walks on networks (graphs), it is a theoretical challenge to explicitly determine the mean first-passage time (MFPT) between two nodes averaged over all pairs. In this paper, we study the MFPT of random walks in the famous…

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…

First passage time plays a fundamental role in dynamical characterization of stochastic processes. Crucially, our current understanding on the problem is almost entirely relies on the theoretical formulations, which assume the processes…

In the present work, we study random walks on complex networks subject to stochastic resetting when the resetting probability is node-dependent. Using a renewal approach, we derive the exact expressions of the stationary occupation…

We examine the aggregate behavior of one-dimensional random walks in a model known as (one-dimensional) Internal Diffusion Limited Aggregation. In this model, a sequence of $n$ particles perform random walks on the integers, beginning at…

We explore first-passage phenomenology for biased active processes with a renewal-type structure, focusing in particular on paradigmatic run-and-tumble models in both discrete and continuous state spaces. In general, we show there is no…

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 investigate reflected random walks in the quarter plane, with particular emphasis on the time spent along the reflection boundary axes. Assuming the drift of the random walk lies within the cone, the local time converges -- without the…

The distribution of the first positive position reached by a random walker starting from the origin is fundamental for understanding the statistics of extremes and records in one-dimensional random walks. We present a comprehensive study of…

We consider a random walk in confined geometry, starting from a site and eventually reaching a target site. We calculate analytically the distribution of the occupation time on a third site, before reaching the target site. The obtained…

We compute exactly the mean number of records $\langle R_N \rangle$ for a time-series of size $N$ whose entries represent the positions of a discrete time random walker on the line. At each time step, the walker jumps by a length $\eta$…

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…