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Motivated by various recent experimental findings, we propose a dynamical model of intermittently self-propelled particles: active particles that recurrently switch between two modes of motion, namely an active run-state and a turn state,…

Soft Condensed Matter · Physics 2025-10-30 Agniva Datta , Carsten Beta , Robert Großmann

We consider random walks in a random environment which are generalized versions of well-known effective models for Mott variable-range hopping. We study the homogenized diffusion constant of the random walk in the one-dimensional case. We…

Probability · Mathematics 2009-09-29 P. Caputo , A. Faggionato

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 introduce a discrete-time random walk model on a one-dimensional lattice with a nonconstant sojourn time and prove that the discrete density converges to a solution of a continuum diffusion equation. Our random walk model is not…

Analysis of PDEs · Mathematics 2023-02-14 Jaywan Chung , Yong-Jung Kim , Min-Gi Lee

We prove quenched invariance principle for simple random walk on the unique infinite percolation cluster for a general class of percolation models on Z^d, d>=2, with long-range correlations introduced in arXiv:1212.2885, solving one of the…

Probability · Mathematics 2015-09-28 Eviatar Procaccia , Ron Rosenthal , Artem Sapozhnikov

We study the maximal displacement of branching random walks in a class of time inhomogeneous environments. Specifically, binary branching random walks with Gaussian increments will be considered, where the variances of the increments change…

Probability · Mathematics 2011-12-07 Ofer Zeitouni , Ming Fang

The diffusive transport of particles in anisotropic media is a fundamental phenomenon in computational, medical and biological disciplines. While deterministic models (partial differential equations) of such processes are well established,…

Computational Physics · Physics 2025-10-20 Luke P. Filippini , Adrianne L. Jenner , Elliot J. Carr

We consider a random walk model in a one-dimensional environment, formed by several zones of finite width with the fixed transition probabilities. It is also assumed that the transitions to the left and right neighboring points have unequal…

Statistical Mechanics · Physics 2017-08-18 A. V. Nazarenko , V. Blavatska

We consider a general discrete-time branching random walk on a countable set X. We relate local, strong local and global survival with suitable inequalities involving the first-moment matrix M of the process. In particular we prove that,…

Probability · Mathematics 2015-05-18 Fabio Zucca

We consider a random walk on a homogeneous Poisson point process with energy marks. The jump rates decay exponentially in the A-power of the jump length and depend on the energy marks via a Boltzmann--like factor. The case A=1 corresponds…

Probability · Mathematics 2015-05-14 P. Caputo , A. Faggionato , T. Prescott

We consider a random walk with transition probabilities weakly dependent on an environment with a deterministic, but strongly chaotic, evolution. We prove that for almost all initial conditions of the environment the walk satisfies the CLT.

Probability · Mathematics 2008-04-23 Dmitry Dolgopyat , Carlangelo Liverani

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

In this work, we are concerned with existence and uniqueness of invariant measures for path-dependent random diffusions and their time discretizations. The random diffusion here means a diffusion process living in a random environment…

Probability · Mathematics 2017-06-20 Jianhai Bao , Jinghai Shao , Chenggui Yuan

We consider a continuous-time random walk which is the generalization, by means of the introduction of waiting periods on sites, of the one-dimensional nonhomogeneous random walk with a position-dependent drift known in the mathematical…

Statistical Mechanics · Physics 2021-10-25 Gaia Pozzoli , Mattia Radice , Manuele Onofri , Roberto Artuso

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 will investigate a random mass splitting model and the closely related random walk in a random environment (RWRE). The heat kernel for the RWRE at time t is the mass splitting distribution at t. We prove a quenched invariance principle…

Probability · Mathematics 2015-09-01 Sayan Banerjee , Christopher Hoffman

We perform simulations for one dimensional continuous-time random walks in two dynamic random environments with fast (independent spin-flips) and slow (simple symmetric exclusion) decay of space-time correlations, respectively. We focus on…

Probability · Mathematics 2012-05-23 L. Avena , P. Thomann

We prove a vector-valued almost sure invariance principle for some classes of time dependent non-uniformly distance expanding dynamical systems. The models we have in mind are certain sequential versions of the smooth non-uniformly distance…

Dynamical Systems · Mathematics 2020-05-14 Yeor Hafouta

We consider a random walker in a dynamic random environment given by a system of independent simple symmetric random walks. We obtain ballisticity results under two types of perturbations: low particle density, and strong local drift on…

We answer the question of Aaronson about the relative complexity of Random Walks in Random Sceneries driven by either aperiodic two dimensional random walks, two-dimensional Simple Random walk, or by aperiodic random walks in the domain of…

Probability · Mathematics 2015-06-02 George Deligiannidis , Zemer Kosloff