Related papers: Persistent random walk on a one-dimensional lattic…
We study random walks evolving in continuous time on a one-dimensional lattice where each site $x$ hosts a quenched random potential $U_x$. The potentials on different sites are independent, identically distributed Gaussian random…
We study quantum walks on general graphs from the point of view of scattering theory. For a general finite graph we choose two vertices and attach one half line to each. We are interested in walks that proceed from one half line, through…
We are interested in the behaviour of the range of the Campanino and P\'etritis random walk, namely a simple random walk on the lattice $\mathbb Z^2$ with random orientations of the horizontal layers. We also study the range of random walks…
In this paper we consider a telegraph equation with time-dependent coefficients, governing the persistent random walk of a particle moving on the line with a time-varying velocity $c(t)$ and changing direction at instants distributed…
We investigate the first passage statistics of active continuous time random walks with Poissonian waiting time distribution on a one dimensional infinite lattice and a two dimensional infinite square lattice. We study the small and large…
The first passage statistics of a continuous time random walker with Poisson distributed jumps on one and two dimensional infinite lattices is investigated. An exact expression for the probability of first return to the origin in one…
We recently demonstrated that standard fixed-time lattice random-walk models cannot be modified to properly represent biased diffusion processes in more than two dimensions. The origin of this fundamental limitation appears to be the fact…
The propagation of light in a resonant atomic vapor can \textit{a priori} be thought of as a multiple scattering process, in which each scattering event redistributes both the direction and the frequency of the photons. Particularly, the…
We show that a signal can propagate in a particular direction through a model random medium regardless of the precise state of the medium. As a prototype, we consider a point particle moving on a one-dimensional lattice whose sites are…
We survey recent results of normal and anomalous diffusion of two types of random motions with long memory in ${\Bbb R}^d$ or ${\Bbb Z}^d$. The first class consists of random walks on ${\Bbb Z}^d$ in divergence-free random drift field,…
Stationary probability distributions of one-dimensional random walks on lattices with aperiodic disorder are investigated. The pattern of the distribution is closely related to the diffusional behavior, which depends on the wandering…
We consider a model of random walk in ${\mathbb Z}^2$ with (fixed or random) orientation of the horizontal lines (layers) and with non constant iid probability to stay on these lines. We prove the transience of the walk for any fixed…
We study Markov chains on a lattice in a codimension-one stratified independent random environment, exploiting results established in [2]. First of all the random walk is transient in dimension at least three. Focusing on dimension two,…
We consider a continuous-time branching random walk on a multidimensional lattice in a random branching medium. It is theoretically known that, in such branching random walks, large rare fluctuations of the medium may lead to anomalous…
Exploiting the coherent medium approximation, random walk among sites distributed randomly in space is investigated when the jump rate depends on the distance between two adjacent sites. In one dimension, it is shown that when the jump rate…
We have studied the diffusion of a single particle on a one-dimensional lattice. It is shown that, for a self-similar distribution of hopping rates, the time dependence of the mean-square displacement follows an anomalous power law…
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…
Persistent random walks are intermediate transport processes between a uniform rectilinear motion and a Brownian motion. They are formed by successive steps of random finite lengths and directions travelled at a fixed speed. The isotropic…
We establish a comprehensive probability theory for coherent transport of random waves through arbitrary linear media. The transmissivity distribution for random coherent waves is a fundamental B-spline with knots at the transmission…
We establish recurrence criteria for sums of independent random variables which take values in Euclidean lattices of varying dimension. In particular, we describe transient inhomogenous random walks in the plane which interlace two…