Related papers: Recurrent random walks on $\mathbb{Z}$ with infini…
We study a simple random walk on Z^2 with constraints on the axis. Motivation comes from physics when particles (a gas for example, see [Dal88]) are submitted to a local field. In our case we assume that the particle evolves freely in the…
We consider a class of strongly edge-reinforced random walks, where the corresponding reinforcement weight function is nondecreasing. It is known, from Limic and Tarr\`{e}s [Ann. Probab. (2007), to appear], that the attracting edge emerges…
We consider a ballistic random walk in an i.i.d. random environment that does not allow retreating in a certain fixed direction. Homogenization and regeneration techniques combine to prove a law of large numbers and an averaged invariance…
Simple random walks on various types of partially horizontally oriented regular lattices are considered. The horizontal orientations of the lattices can be of various types (deterministic or random) and depending on the nature of the…
We consider random walk on the structure given by a random hypergraph in the regime where there is a unique giant component. We give the asymptotics for hitting times, cover times, and commute times and show that the results obtained for…
Random walks on a group $G$ model many natural phenomena. A random walk is defined by a probability measure $p$ on $G$. We are interested in asymptotic properties of the random walks and in particular in the linear drift and the asymptotic…
We consider a vertex reinforced random walk on the integer lattice with sub-linear reinforcement. Under some assumptions on the regular variation of the weight function, we characterize whether the walk gets stuck on a finite interval. When…
We consider three kinds of discrete-time arrival processes: transient, intermediate and recurrent, characterized by a finite, possibly finite and infinite number of events, respectively. In this context, we study renewal processes which are…
A random walk on a $N$-dimensional hypercube is a discrete time stochastic process whose state space is the set $\{-1,+1\}^{N}$, which has uniform probability of reaching any neighbour state, and probability zero of reaching a non-neighbour…
Random walk on changing graphs is considered. For sequences of finite graphs increasing monotonically towards a limiting infinite graph, we establish transition probability upper bounds. It yields sufficient transience criteria for simple…
In this work, we study open quantum random walks, as described by S. Attal et al. These objects are given in terms of completely positive maps acting on trace-class operators, leading to one of the simplest open quantum versions of the…
We study biased random walk on the infinite connected component of supercritical percolation on the integer lattice $\mathbb{Z}^d$ for $d\geq 2$. For this model, Fribergh and Hammond showed the existence of an exponent $\gamma$ such that:…
A previous paper (hep-lat/9311011) proposed a new kind of random walk on a spherically-symmetric lattice in arbitrary noninteger dimension $D$. Such a lattice avoids the problems associated with a hypercubic lattice in noninteger dimension.…
Asymptotic estimates of the hitting distribution of a long segment on the real axis for two dimensional random walks on ${\bf Z}^2$ of zero mean and finite variances are obtained: some are general and exhibit its apparent similarity to the…
The presence of temporal correlations in random movement trajectories is a widespread phenomenon across biological, chemical and physical systems. The ubiquity of persistent and anti-persistent motion in many natural and synthetic systems…
We consider a random walk on a second countable locally compact topological space endowed with an invariant Radon measure. We show that if the walk is symmetric and if every subset which is invariant by the walk has zero or infinite…
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 consider an exactly solvable model of branching random walk with random selection, which describes the evolution of a population with $N$ individuals on the real line. At each time step, every individual reproduces independently, and its…
In this paper we continue our study of a multidimensional random walk with zero mean and finite variance killed on leaving a cone. We suggest a new approach that allows one to construct a positive harmonic function in Lipschitz cones under…
We study persistent random walk with time dependent velocity reversal probabilities and identify a criterion for a non-equilibrium dynamical transition. As a representative example, we consider a power law reversal probability $p(t)\sim…