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We study a random walk on $\mathbb{Z}$ which evolves in a dynamic environment determined by its own trajectory. Sites flip back and forth between two modes, $p$ and $q$. $R$ consecutive right jumps from a site in the $q$-mode are required…

Probability · Mathematics 2015-03-05 Ross G. Pinsky , Nicholas F. Travers

We study a $d$-dimensional branching random walk (BRW) in an i.i.d. random environment on $\mathbb{Z}^d$ in discrete time. A Bernoulli trap field is attached to $\mathbb{Z}^d$, where each site, independently of the others, is a trap with a…

Probability · Mathematics 2026-01-12 Mehmet Öz

This is the third in a series of papers in which we consider one-dimensional Random Walk in Cooling Random Environment (RWCRE). The latter is obtained by starting from one-dimensional Random Walk in Random Environment (RWRE) and resampling…

Probability · Mathematics 2019-07-26 Luca Avena , Yuki Chino , Conrado da Costa , Frank den Hollander

In this paper, we derive the distribution of a two-dimensional (complex) random walk in which the angle of each step is restricted to a subset of the circle. This setting appears in various domains, such as in over-the-air computation in…

Signal Processing · Electrical Eng. & Systems 2026-05-18 Karl-Ludwig Besser

Random walks in random sceneries (RWRS) are simple examples of stochastic processes in disordered media. They were introduced at the end of the 70's by Kesten-Spitzer and Borodin, motivated by the construction of new self-similar processes…

Probability · Mathematics 2014-09-29 Nadine Guillotin-Plantard , Julien Poisat , Renato Soares Dos Santos

We focus on the study of dynamics of two kinds of random walk: generic random walk (GRW) and maximal entropy random walk (MERW) on two model networks: Cayley trees and ladder graphs. The stationary probability distribution for MERW is given…

Statistical Mechanics · Physics 2012-06-01 Jeremi K. Ochab

A constrained diffusive random walk of n steps and a random flight in Rd, which can be expressed in the same terms, were investigated independently in recent papers. The n steps of the walk are identically and independently distributed…

Statistical Mechanics · Physics 2010-07-28 G. Le Caer

We consider a one-dimensional recurrent random walk in random environment (RWRE) when the environment is i.i.d. with a parametric, finitely supported distribution. Based on a single observation of the path, we provide a maximum likelihood…

Probability · Mathematics 2014-04-10 Francis Comets , Mikael Falconnet , Oleg Loukianov , Dasha Loukianova

Based on studies on four specific networks, we conjecture a general relation between the walk dimensions $d_{w}$ of discrete-time random walks and quantum walks with the (self-inverse) Grover coin. In each case, we find that $d_{w}$ of the…

Statistical Mechanics · Physics 2015-06-03 Stefan Boettcher , Stefan Falkner , Renato Portugal

We consider simple random walks on random graphs embedded in $\mathbb{R}^d$ and generated by point processes such as Delaunay triangulations, Gabriel graphs and the creek-crossing graphs. Under suitable assumptions on the point process, we…

Probability · Mathematics 2015-06-19 Arnaud Rousselle

We describe a universal transition mechanism characterizing the passage to an annealed behavior and to a regime where the fluctuations about this behavior are Gaussian, for the long time asymptotics of the empirical average of the expected…

Probability · Mathematics 2007-07-04 Gerard Ben Arous , Stanislav Molchanov , Alejandro F. Ramirez

We prove a law of large numbers for random walks in certain kinds of i.i.d. random environments in Z^d that is an extension of a result of Bolthausen, Sznitman and Zeitouni (2003). We use this result, along with the lace expansion for…

Probability · Mathematics 2016-11-25 Mark Holmes , Rongfeng Sun

A $\delta$ once-reinforced random walk ($\delta$-ORRW) on connected graph is a self-interacting random walk which moves to its neighbors at each step according to the weights of the edges at that time, where the weights are $1$ on edges…

Probability · Mathematics 2026-03-30 Xiangyu Huang , Yong Liu , Kainan Xiang

We extend our study of random walks and induced Dirichlet forms on self-similar sets [arXiv:1604.05440, 1612.01708] to compact spaces of homogeneous type $(K, \rho ,\mu)$. A successive partition on $K$ brings a natural augmented tree…

Probability · Mathematics 2018-04-10 Shi-Lei Kong , Ka-Sing Lau , Ting-Kam Leonard Wong

We propose random walks on suitably defined graphs as a framework for finescale modeling of particle motion in an obstructed environment where the particle may have interactions with the obstructions and the mean path length of the particle…

Probability · Mathematics 2019-10-25 Preston Donovan , Muruhan Rathinam

The paper consists of two parts. In the first part we review recent work on limit theorems for random walks in random environment (RWRE) on a strip with jumps to the nearest layers. In the second part, we prove the quenched Local Limit…

Probability · Mathematics 2019-10-30 Dmitry Dolgopyat , Ilya Goldsheid

We consider weighted geodesic random walks in a complete Riemannian manifold $(M,g)$. We show that for almost all sequences of weights (with respect to a suitable measure), these weighted geodesic random walks satisfy, when suitably scaled,…

Probability · Mathematics 2026-02-20 Rik Versendaal

We consider a model, introduced by Boldrighini, Minlos and Pellegrinotti, of random walks in dynamical random environments on the integer lattice Z^d with d>=1. In this model, the environment changes over time in a Markovian manner,…

Probability · Mathematics 2007-05-23 Antar Bandyopadhyay , Ofer Zeitouni

We consider a random walk among a Poisson system of moving traps on ${\mathbb Z}$. In earlier work [DGRS12], the quenched and annealed survival probabilities of this random walk have been investigated. Here we study the path of the random…

Probability · Mathematics 2017-02-01 Siva Athreya , Alexander Drewitz , Rongfeng Sun

We derive an annealed large deviation principle for the normalised local times of a continuous-time random walk among random conductances in a finite domain in $\Z^d$ in the spirit of Donsker-Varadhan \cite{DV75}. We work in the interesting…

Probability · Mathematics 2011-04-11 Wolfgang König , Michele Salvi , Tilman Wolff
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