Related papers: Q-zero range has random walking shocks

We consider a one-dimensional totally asymmetric nearest-neighbor zero-range process with site-dependent jump-rates - an environment. For each environment p we prove that the set of all invariant measures is the convex hull of a set of…

In this paper we observe the frog model, an infinite system of interacting random walks, on Z with an asymmetric underlying random walk. Under the assumption of transience with a fixed frog distribution, we construct an explicit formula for…

We investigate the use of discrete-time quantum walks to sample from an almost-uniform distribution, in the absence of any external source of randomness. Integers are encoded on the vertices of a cycle graph, and a quantum walker evolves…

The unpredictability of quantum physics gives rise to intrinsic randomness. In an adversarial scenario, any additional degrees of freedom must be attributed to an eavesdropper with correlations to the measurement set-up. The true randomness…

We consider the one-dimensional partially asymmetric exclusion process with random hopping rates, in which a fraction of particles (or sites) have a preferential jumping direction against the global drift. In this case the accumulated…

A continuous-time random walk in the quarter plane with homogeneous transition rates is considered. Given a non-negative reward function on the state space, we are interested in the expected stationary performance. Since a direct derivation…

A random walk is known as a random process which describes a path including a succession of random steps in the mathematical space. It has increasingly been popular in various disciplines such as mathematics and computer science.…

This paper presents the exact expressions of the transition probabilities of some non-determinantal Bethe ansatz solvable interacting particle systems: the two-sided PushASEP, the asymmetric avalanche process and the asymmetric zero range…

We study the random walk $X$ on the range of a simple random walk on $\mathbb{Z}^d$ in dimensions $d\geq 4$. When $d\geq 5$ we establish quenched and annealed scaling limits for the process $X$, which show that the intersections of the…

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…

In this article, we study linearly edge-reinforced random walk on general multi-level ladders for large initial edge weights. For infinite ladders, we show that the process can be represented as a random walk in a random environment, given…

Numerical and theoretical studies of a one-dimensional spin model with locally broken spin symmetry are presented. The multi-species annihilating random walk transition found at zero branching rate previously is investigated now concerning…

Using coordinate-free basic operators on toy Fock spaces \cite{AP}, quantum random walks are defined following the ideas in \cite{LP,AP}. Strong convergence of quantum random walks associated with bounded structure maps is proved under…

In this paper we study activity fluctuations in an asymmetric death-branching process in one-dimension. The model, which is a variant of the asymmetric Glauber model, has already been studied in [12]. It is known that in the low-activity…

Famously, a $d$-dimensional, spatially homogeneous random walk whose increments are non-degenerate, have finite second moments, and have zero mean is recurrent if $d \in \{1,2\}$ but transient if $d \geq 3$. Once spatial homogeneity is…

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 define a dynamical simple symmetric random walk in one dimension, and show that there almost surely exist exceptional times at which the walk tends to infinity. This is in contrast to the usual dynamical simple symmetric random walk in…

Random walks as well as diffusions in random media are considered. Methods are developed that allow one to establish large deviation results for both the `quenched' and the `averaged' case.

We construct random point processes in the complex plane that are asymptotically close to a given doubling measure. The processes we construct are the zero sets of random entire functions that are constructed through generalised Fock…

Consider the extreme value of a Bernoulli random walk on the one-dimensional integer lattice, with reflection at 0, over a finite discrete time interval. Only the asymmetric (biased) case is discussed. Asymptotic mean/variance results are…