Related papers: Urn-related random walk with drift $\rho x^{\alpha…

The random walk to be considered takes place in the d- spherical dual of the group U(n + 1), for a fixed finite dimensional irreducible representation d of U(n). The transition matrix comes from the three term recursion relation satisfied…

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 introduce a multi-coin discrete quantum random walk where the amplitude for a coin flip depends upon previous tosses. Although the corresponding classical random walk is unbiased, a bias can be introduced into the quantum walk by varying…

We consider a variation of the Generalized Excited Random Walk (GERW) in dimension $d\ge 2$ where the lower bound on the drift for excited jumps is time-dependent and decays to zero. We show that if the lower bound decays slower that…

We give criteria for ergodicity, transience and null recurrence for the random walk in random environment on {0,1,2,...}, with reflection at the origin, where the random environment is subject to a vanishing perturbation. Our results…

This investigation is motivated by a result we proved recently for the random transposition random walk: the distance from the starting point of the walk has a phase transition from a linear regime to a sublinear regime at time $n/2$. Here,…

We study one-dimensional excited random walks with non-nearest neighbor jumps. When the process is at a vertex that has not been visited before, its next transition has a positive drift to the right, possibly with long jumps. Whenever the…

We study random walks on Erd\"os-R\'enyi random graphs in which, every time the random walk returns to the starting point, first an edge probability is independently sampled according to a priori measure $\mu$, and then an Erd\"os-R\'enyi…

Nonintersecting Brownian bridges on the unit circle form a determinantal stochastic process exhibiting random matrix statistics for large numbers of walkers. We investigate the effect of adding a drift term to walkers on the circle…

We investigate fluid transport in random velocity fields with unsteady drift. First, we propose to quantify fluid transport between flow regimes of different characteristic motion, by escape probability and mean residence time. We then…

We study whether the probability distribution of a discrete quantum walk can get arbitrarily close to uniform, given that the walk starts with a uniform superposition of the outgoing arcs of some vertex. We establish a characterization of…

The paper considers excited random walks (ERWs) on integers in i.i.d. environments with a bounded number of excitations per site. The emphasis is primarily on the critical case for the transition between recurrence and transience which…

Consider the first exit time of one-dimensional Brownian motion $\{B_s\}_{s\geq 0}$ from a random passageway. We discuss a Brownian motion with two time-dependent random boundaries in quenched sense. Let $\{W_s\}_{s\geq 0}$ be an other…

In this paper we consider a stochastic process that may experience random reset events which bring suddenly the system to the starting value and analyze the relevant statistical magnitudes. We focus our attention on monotonous…

In part I (math.PR/0406392) we proved for an arbitrary one-dimensional random walk with independent increments that the probability of crossing a level at a given time n is of the maximal order square root of n. In higher dimensions we call…

We analyze the dynamics of random walks in which the jumping probabilities are periodic {\it time-dependent} functions. In particular, we determine the survival probability of biased walkers who are drifted towards an absorbing boundary.…

Let $X = (X_1, X_2)$ be a 2-dimensional random variable and $X(n), n \in \mathbb{N}$ a sequence of i.i.d. copies of $X$. The associated random walk is $S(n)= X(1) + \cdots +X(n)$. The corresponding absorbed-reflected walk $W(n), n \in…

The deterministic random walk is a deterministic process analogous to a random walk. While there are some results on the cover time of the rotor-router model, which is a deterministic random walk corresponding to a simple random walk,…

We consider a population of $N$ labeled random walkers moving on a substrate, and an excitation jumping among the walkers upon contact. The label $\mathcal{X}(t)$ of the walker carrying the excitation at time $t$ can be viewed as a…

Planar run-and-tumble walks with orthogonal directions of motion are considered. After formulating the problem with generic transition probabilities among the orientational states, we focus on the symmetric case, giving general expressions…