English
Related papers

Related papers: Random walk in random environment in a two-dimensi…

200 papers

The random walk process in a nonhomogeneous medium, characterised by a L\'evy stable distribution of jump length, is discussed. The width depends on a position: either before the jump or after that. In the latter case, the density slope is…

Statistical Mechanics · Physics 2017-03-29 Tomasz Srokowski

This paper has two main results, which are connected through the fact that the first is a key ingredient in the second. Both are extensions of results concerning directional transience of nearest-neighbor random walks in random environments…

Probability · Mathematics 2023-10-31 Daniel J. Slonim

Two-dimensional networks of ordered quantum dots beyond the percolation threshold are studied, as typical example of conducting nanostructures with quenched random disorder. Theory predicts anomalous diffusion with stretched-exponential…

Statistical Mechanics · Physics 2016-01-06 Fabrizio Cleri

We consider a random walk on Z^d in an i.i.d. balanced random environment, that is a random walk for which the probability to jump from x to nearest neighbor x+e is the same as to nearest neighbor x-e. Assuming that the environment is…

Probability · Mathematics 2012-07-05 Noam Berger , Jean-Dominique Deuschel

We study the Ergodic Properties of Random Walks in stationary ergodic environments without uniform ellipticity under a minimal assumption. There are two main components in our work. The first step is to adopt the arguments of Lawler to…

Probability · Mathematics 2026-02-03 Ayan Ghosh

We introduce the pushy random walk, where a walker can push multiple obstacles, thereby penetrating large distances in environments with finite obstacle density. This process provides a minimal model for experimentally observed interactions…

Statistical Mechanics · Physics 2026-04-07 Ofek Lauber Bonomo , Itamar Shitrit , Shlomi Reuveni , Sidney Redner

We introduce an exactly-solvable model of random walk in random environment that we call the Beta RWRE. This is a random walk in $\mathbb{Z}$ which performs nearest neighbour jumps with transition probabilities drawn according to the Beta…

Probability · Mathematics 2021-05-19 Guillaume Barraquand , Ivan Corwin

We are concerned with random walks on $\mathbb{Z}^d$, $d\geq 3$, in an i.i.d. random environment with transition probabilities $\epsilon$-close to those of simple random walk. We assume that the environment is balanced in one fixed…

Probability · Mathematics 2016-12-28 Erich Baur

We consider a one dimensional random walk in random environment that is uniformly biased to one direction. In addition to the transition probability, the jump rate of the random walk is assumed to be spatially inhomogeneous and random. We…

Probability · Mathematics 2018-11-27 Amir Dembo , Ryoki Fukushima , Naoki Kubota

We study, on a $d$ dimensional hypercubic lattice, a random walk which is homogeneous except for one site. Instead of visiting this site, the walker hops over it with arbitrary rates. The probability distribution of this walk and the…

Statistical Mechanics · Physics 2009-10-31 R. K. P. Zia , Z. Toroczkai

We consider a model for random walks on random environments (RWRE) with random subset of the d-dimensional Euclidean lattice as the vertices, and uniform transition probabilities on 2d points (two "coordinate nearest points" in each of the…

Probability · Mathematics 2011-10-27 Ron Rosenthal

We consider a model for random walks on random environments (RWRE) with random subset of Z^d as the vertices, and uniform transition probabilities on 2d points (two "coordinate nearest points" in each of the d coordinate directions). We…

Probability · Mathematics 2015-09-08 Noam Berger , Ron Rosenthal

We study the evolution of a random walker on a conservative dynamic random environment composed of independent particles performing simple symmetric random walks, generalizing results of [16] to higher dimensions and more general transition…

We derive a quenched invariance principle for random walks in random environments whose transition probabilities are defined in terms of weighted cycles of bounded length. To this end, we adapt the proof for random walks among random…

Probability · Mathematics 2008-12-18 Jean-Dominique Deuschel , Holger Kösters

In [3] the radius of convergence of the generating function of the collision local time of two independent copies of an irreducible, symmetric and transient random walk on Zd, d \geq 1, was studied. Two versions were considered: z1, the…

Probability · Mathematics 2012-06-11 Frank den Hollander , Alex A. Opoku

According to Comets, Gantert and Zeitouni on the one hand and to Derriennic on the other hand, some functionals associated to the hitting times of random walks in random environment on the integer line coincide, for the walk itself and for…

Probability · Mathematics 2016-09-07 Didier Piau

Models of random walks are considered in which walkers are born at one location and die at all other locations with uniform death rate. Steady-state distributions of random walkers exhibit dimensionally dependent critical behavior as a…

High Energy Physics - Lattice · Physics 2009-09-25 Carl M. Bender , Stefan Boettcher , Peter N. Meisinger

We consider random walks in a random environment of the type p_0+\gamma\xi_z, where p_0 denotes the transition probabilities of a stationary random walk on \BbbZ^d, to nearest neighbors, and \xi_z is an i.i.d. random perturbation. We give…

Probability · Mathematics 2007-05-23 Christophe Sabot

We study continuous-time (variable speed) random walks in random environments on $\mathbb{Z}^d$, $d\ge2$, where, at time $t$, the walk at $x$ jumps across edge $(x,y)$ at time-dependent rate $a_t(x,y)$. The rates, which we assume stationary…

Probability · Mathematics 2020-01-06 Marek Biskup , Pierre-François Rodriguez

Random walks represent an important tool for probing the structural and dynamical properties of networks and modeling transport and diffusion processes on networks. However, when individuals' movement becomes dictated by more complicated…

Pattern Formation and Solitons · Physics 2022-11-24 Per Sebastian Skardal