Related papers: Path Coalescence in Spatially Correlated Random Wa…

We investigate continuous-time quantum walks of two indistinguishable particles (bosons, fermions or hard-core bosons) in one-dimensional lattices with nearest-neighbour interactions. The two interacting particles can undergo independent-…

We introduce random walks in a sparse random environment on $\mathbb Z$ and investigate basic asymptotic properties of this model, such as recurrence-transience, asymptotic speed, and limit theorems in both the transient and recurrent…

Quantum walks on graphs can model physical processes and serve as efficient tools in quantum information theory. Once we admit random variations in the connectivity of the underlying graph, we arrive at the problem of percolation, where the…

We study a family of correlated one-dimensional random walks with a finite memory range M.These walks are extensions of the Taylor's walk as investigated by Goldstein, which has a memory range equal to one. At each step, with a probability…

We theoretically study the transport properties of self-propelled particles on complex structures, such as motor proteins on filament networks. A general master equation formalism is developed to investigate the persistent motion of…

In this paper we create a model of particle motion on a three-dimensional lattice using discrete random walk with small steps. We rigorously construct a probability space of the particle trajectories. Unlike deterministic approach in…

The probability distribution p(l) of an atom to return to a step at distance l from the detachment site, with a random walk in between, is exactly enumerated. In particular, we study the dependence of p(l) on step roughness, presence of…

Random walks on general graphs play an important role in the understanding of the general theory of stochastic processes. Beyond their fundamental interest in probability theory, they arise also as simple models of physical systems. A brief…

We discuss conditions for unique ergodicity of a collective random walk on a continuous circle. Individual particles in this collective motion perform independent (and different in general) random walks conditioned by the assumption that…

Random walks with memory typically involve rules where a preference for either revisiting or avoiding those sites visited in the past are introduced somehow. Such effects have a direct consequence on the statistics of first-passage and…

This work is motivated by the study of some two-dimensional random walks in random environment (RWRE) with transition probabilities independent of one coordinate of the walk. These are non-reversible models and can not be treated by…

Activated Random Walk is a system of interacting particles which presents a phase transition and a conjectured phenomenon of self-organized criticality. In this note, we prove that, in dimension 1, in the supercritical case, when a segment…

We consider random walks in dynamic random environments, with an environment generated by the time-reversal of a Markov process from the oriented percolation universality class. If the influence of the random medium on the walk is small in…

We study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are…

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…

Although the theoretical behavior of one-dimensional random walks in random environments is well understood, the numerical evaluation of various characteristics of such processes has received relatively little attention. This paper develops…

A discrete time quantum walker is considered in one dimension, where at each step, the translation can be more than one unit length chosen randomly. In the simplest case, the probability that the distance travelled is $\ell$ is taken as…

We consider a three dimensional system consisting of a large number of small spherical particles, distributed in a range of sizes and heights (with uniform distribution in the horizontal direction). Particles move vertically at a…

The common perception is that strong coupling to the environment will always render the evolution of the system density matrix quasi-classical (in fact, diffusive) in the long time limit. We present here a counter-example, in which a…

In empirical studies of random walks, continuous trajectories of animals or individuals are usually sampled over a finite number of points in space and time. It is however unclear how this partial observation affects the measured…