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We consider biased random walks on random networks constituted by a random comb comprising a backbone with quenched-disordered random-length branches. The backbone and the branches run in the direction of the bias. For the bare model as…

Statistical Mechanics · Physics 2025-06-09 Mrinal Sarkar , Shamik Gupta

A switching random walk, commonly known under the misnomer `oscillating random walk', is a real-valued Markov chain whose distribution of increments is determined by the sign of the current position. We explicitly identify an invariant…

Probability · Mathematics 2025-06-10 Vladislav Vysotsky

We investigate the occurrence of anomalous diffusive transport associated with acoustic wave fields propagating through highly-scattering periodic media. Previous studies had correlated the occurrence of anomalous diffusion to either the…

Disordered Systems and Neural Networks · Physics 2019-03-27 Salvatore Buonocore , Mihir Sen , Fabio Semperlotti

We investigate active lattice walks: biased continuous time random walks which perform orientational diffusion between lattice directions in one and two spatial dimensions. We study the occupation probability of an arbitrary site on the…

Statistical Mechanics · Physics 2024-02-27 Stephy Jose , Dipanjan Mandal , Mustansir Barma , Kabir Ramola

Bias plays an important role in the enhancement of diffusion in periodic potentials. Using the continuous-time random walk in the presence of a bias, we provide a novel mechanism for the enhancement of diffusion in a random energy…

Statistical Mechanics · Physics 2018-08-15 Takuma Akimoto , Andrey G. Cherstvy , Ralf Metzler

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

Stochastic particle--based models are useful tools for describing the collective movement of large crowds of pedestrians in crowded confined environments. Using descriptions based on the simple exclusion process, two populations of…

Statistical Mechanics · Physics 2020-08-26 Emilio N. M. Cirillo , Matteo Colangeli , Adrian Muntean , T. K. Thoa Thieu

Pathways of diffusion observed in real-world systems often require stochastic processes going beyond first-order Markov models, as implicitly assumed in network theory. In this work, we focus on second-order Markov models, and derive an…

Physics and Society · Physics 2014-01-03 Renaud Lambiotte , Vsevolod Salnikov , Martin Rosvall

Resetting or restart, when applied to a stochastic process, usually brings its dynamics to a time-independent stationary state. In turn, the optimal resetting rate makes the mean time to reach a target to be the shortest one. These and…

Statistical Mechanics · Physics 2022-08-31 Przemyslaw Chelminiak

The characterization of record events is considered for a discrete-time random walk model with long-term memory arising from correlations between successive steps. An important feature is that the correlations are strong enough to give rise…

Statistical Mechanics · Physics 2021-02-02 Michael J. Kearney

We consider the problem of the first passage time to the origin of a spatially non-homogeneous random walk with a position-dependent drift, known as the Gillis random walk, in the presence of resetting. The walk starts from an initial site…

Probability · Mathematics 2022-12-09 Mattia Radice

Stochastic interactions generically enhance self-diffusivity in living and biological systems, e.g. optimizing navigation strategies and controlling material properties of cellular tissues and bacterial aggregates. Despite this, the…

Soft Condensed Matter · Physics 2024-01-24 Henry Alston , Thibault Bertrand

Random walks provide a simple conventional model to describe various transport processes, for example propagation of heat or diffusion of matter through a medium. However, in many practical cases the medium is highly irregular due to…

Probability · Mathematics 2019-06-10 L. V. Bogachev

We studied simple random-walk models with asymmetric time delays. Stochastic simulations were performed for hyperbolic-tangent fitness functions and to obtain analytical results we approximated them by step functions. A novel behavior has…

Statistical Mechanics · Physics 2025-05-30 Kamil Łopuszański , Jacek Miękisz

We look into the problem of stochastic resetting with refractory periods. The model dynamics comprises diffusive and motionless phases. The diffusive phase ends at random time instants, at which the system is reset to a given position --…

Statistical Mechanics · Physics 2024-03-26 Gregorio García-Valladares , Deepak Gupta , Antonio Prados , Carlos A. Plata

Standard continuous time random walk (CTRW) models are renewal processes in the sense that at each jump a new, independent pair of jump length and waiting time are chosen. Globally, anomalous diffusion emerges through action of the…

Statistical Mechanics · Physics 2015-06-17 Johannes HP Schulz , Aleksei V Chechkin , Ralf Metzler

We study the asymptotic distribution of random walks on $\mathbb Z^d$ ($d\ge1$) in deterministic reversible environments defined by an assignment of a positive conductance to each edge of $\mathbb Z^d$. We identify a deterministic set of…

Probability · Mathematics 2025-12-03 Marek Biskup

A new model of search based on stochastic resetting is introduced, wherein rate of resets depends explicitly on time elapsed since the beginning of the process. It is shown that rate inversely proportional to time leads to paradoxical…

Statistical Mechanics · Physics 2019-09-11 Łukasz Kuśmierz , Taro Toyoizumi

We calculate the diffusion coefficients of persistent random walks on lattices, where the direction of a walker at a given step depends on the memory of a certain number of previous steps. In particular, we describe a simple method which…

Statistical Mechanics · Physics 2013-02-07 Thomas Gilbert , David P. Sanders

Random walk subject to random drive has been extensively employed as a model for physical and biological processes. While equilibrium statistical physics has yielded significant insights into the distributions of dynamical fixed points of…

Statistical Mechanics · Physics 2023-11-22 Zijun Li , Jiming Yang , Huiyu Li