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Inspired by problems in biochemical kinetics, we study statistical properties of an overdamped Langevin process whose friction coefficient depends on the state of a similar, unobserved process. Integrating out the latter, we derive the long…

Statistical Mechanics · Physics 2009-08-13 Golan Bel , Ilya Nemenman

We study the ergodic properties of two classes of random dynamical systems: a type of Markov chain which we call the \textit{alternating random walk} and a certain stochastic billiard system which describes the motion of a free-moving rough…

Dynamical Systems · Mathematics 2024-01-02 Peter Rudzis

Understanding how simple local interactions give rise to emergent exploration patterns is a fundamental question in statistical physics. We introduce a minimal model of two coupled agents that avoid retracing their own paths while being…

Populations and Evolution · Quantitative Biology 2026-03-24 Nick Dashti , M. N. Najafi , Debra J. Searles

Ergodicity is a fundamental issue for a stochastic process. In this paper, we refine results on ergodicity for a general type of Markov chain to a specific type or the $GI/G/1$-type Markov chain, which has many interesting and important…

Probability · Mathematics 2012-08-28 YongHua Mao , Yongming Tai , Yiqiang Q. Zhao , Jiezhong Zou

In single-particle tracking experiments measuring anomalous diffusion dynamics, understanding ergodicity is crucial, as it ensures that the time average of an observable matches the ensemble average, and can thus be fitted with known…

Statistical Mechanics · Physics 2026-03-25 Wei Wang , Qing Wei , Igor M. Sokolov , Ralf Metzler , Aleksei Chechkin

The existence of the {\em typical set} is key for data compression strategies and for the emergence of robust statistical observables in macroscopic physical systems. Standard approaches derive its existence from a restricted set of…

Statistical Mechanics · Physics 2022-02-10 Rudolf Hanel , Bernat Corominas-Murtra

We establish a connection between exclusion statistics with arbitrary integer exclusion parameter $g$ and a class of random walks on planar lattices. This connection maps the generating function for the number of closed walks of given…

Statistical Mechanics · Physics 2020-03-06 Stephane Ouvry , Alexios P. Polychronakos

We present a numerical study of a two-lane version of the stochastic non-equilibrium model known as the totally asymmetric simple exclusion process. For such a system with open boundaries, and suitably chosen values of externally-imposed…

Statistical Mechanics · Physics 2019-07-31 S. L. A. de Queiroz , R. B. Stinchcombe

We analyse large deviations of time-averaged quantities in stochastic processes with long-range memory, where the dynamics at time t depends itself on the value q_t of the time-averaged quantity. First we consider the elephant random walk…

Statistical Mechanics · Physics 2020-08-05 Robert L. Jack , Rosemary J. Harris

Stochastic reaction networks are mathematical models frequently used in, but not limited to, biochemistry. These models are continuous-time Markov chains whose transition rates depend on certain parameters called rate constants, which…

Probability · Mathematics 2025-08-14 Daniele Cappelletti , Aidan Howells , Chuang Xu

The exclusion process in which particles may jump any distance l>=1 with the probability that decays as l^-(1+sigma) is studied from coarse-grained equation for density profile in the limit when the lattice spacing goes to zero. For…

Statistical Mechanics · Physics 2008-05-16 J. Szavits-Nossan , K. Uzelac

We study how an evanescence process affects the number of distinct sites visited by a continuous time random walker in one dimension. We distinguish two very different cases, namely, when evanescence can only occur concurrently with a jump,…

Statistical Mechanics · Physics 2015-06-17 E. Abad , S. B. Yuste , Katja Lindenberg

We study the enhanced diffusivity in the so called elephant random walk model with stops (ERWS) by including symmetric random walk steps at small probability $\epsilon$. At any $\epsilon > 0$, the large time behavior transitions from…

Probability · Mathematics 2017-05-09 Jiancheng Lyu , Jack Xin , Yifeng Yu

The effects of purely elastic collisions on the dynamics of heavy inertial particles is investigated in a three-dimensional random incompressible flow. It is shown that the statistical properties of inter-particle separations and relative…

Fluid Dynamics · Physics 2015-06-12 Jeremie Bec , Stefano Musacchio , Samriddhi Sankar Ray

Some stochastic systems are particularly interesting as they exhibit critical behavior without fine-tuning of a parameter, a phenomenon called self-organized criticality. In the context of driven-dissipative steady states, one of the main…

Probability · Mathematics 2020-09-29 Leonardo T. Rolla

The Edwards hypothesis of ergodicity of blocked configurations for gently tapped granular materials is tested for abstract models of spin systems on random graphs and spin chains with kinetic constraints. The tapping dynamics is modeled by…

Statistical Mechanics · Physics 2009-11-07 Johannes Berg , Silvio Franz , Mauro Sellitto

Recent molecular dynamics simulations show that a dilute relativistic gas equilibrates to a Juettner velocity distribution if ensemble velocities are measured simultaneously in the observer frame. The analysis of relativistic Brownian…

Statistical Mechanics · Physics 2013-02-04 David Cubero , Joern Dunkel

We consider a one-dimensional continuous time random walk with transition rates depending on an underlying autonomous simple symmetric exclusion process starting out of equilibrium. This model represents an example of a random walk in a…

Probability · Mathematics 2016-11-26 Luca Avena , Tertuliano Franco , Milton Jara , Florian Völlering

This paper summarizes results and some open problems about the large-scale and long-time behavior of asymmetric, disordered exclusion and zero-range processes. These processes have randomly chosen jump rates at the sites of the underlying…

Probability · Mathematics 2007-05-23 Timo Seppalainen

We study semi-infinite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction…

Probability · Mathematics 2024-12-20 Mikhail Menshikov , Serguei Popov , Andrew Wade