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Let $(\xi_n)_{n=0}^\infty$ be a nonhomogeneous Markov chain taking values from finite state-space of $\mathbf{X}=\{1,2,\ldots,b\}$. In this paper, we will study the generalized entropy ergodic theorem with almost-everywhere and…

Probability · Mathematics 2015-01-19 Zhongzhi Wang , Weiguo Yang

We present limit theorems for a sequence of Piecewise Deterministic Markov Processes (PDMPs) taking values in a separable Hilbert space. This class of processes provides a rigorous framework for stochastic spatial models in which discrete…

Probability · Mathematics 2012-04-13 Martin G. Riedler , Michèle Thieullen , Gilles Wainrib

We show the variational convergence of an irreversible Markov jump process describing a finite stochastic particle system to the solution of a countable infinite system of deterministic time-inhomogeneous quadratic differential equations…

Analysis of PDEs · Mathematics 2025-07-08 Jasper Hoeksema , Chun Yin Lam , André Schlichting

Employing large deviation theory, we explore current fluctuations of underdamped Brownian motion for the paradigmatic example of a single particle in a one dimensional periodic potential. Two different approaches to the large deviation…

Statistical Mechanics · Physics 2018-03-12 Lukas P. Fischer , Patrick Pietzonka , Udo Seifert

We consider temporal models of rapidly changing Markovian networks modulated by time-evolving spatially dependent kernels that define rates for edge formation and dissolution. Alternatively, these can be viewed as Markovian networks with…

Probability · Mathematics 2025-06-11 Shankar Bhamidi , Amarjit Budhiraja , Souvik Ray

Current is a characteristic feature of nonequilibrium systems. In stochastic systems, these currents exhibit fluctuations constrained by the rate of dissipation in accordance with the recently discovered thermodynamic uncertainty relation.…

Statistical Mechanics · Physics 2017-10-30 Todd R. Gingrich , Jordan M. Horowitz

We use the $f-divergence$ also called relative entropy as a measure of diversity between probability densities and review its basic properties. In the sequence we define a few objects which capture relevant information from the sample of a…

Statistics Theory · Mathematics 2012-06-20 A. R. Baigorri , C. R. Goncalves , P. A. A. Resende

We study the fluctuations of systems modeled by Markov jump processes with periodic generators. We focus on observables defined through time-periodic functions of the system's states or transitions. Using large deviation theory, canonical…

Statistical Mechanics · Physics 2020-04-22 Lydia Chabane , Raphaël Chétrite , Gatien Verley

The large deviation function for entropy production is calculated for a particle driven along a periodic potential by solving a time-independent eigenvalue problem. In an intermediate force regime, the large deviation function shows…

Statistical Mechanics · Physics 2009-01-15 Jakob Mehl , Thomas Speck , Udo Seifert

We describe a simple form of importance sampling designed to bound and compute large-deviation rate functions for time-extensive dynamical observables in continuous-time Markov chains. We start with a model, defined by a set of rates, and a…

Statistical Mechanics · Physics 2019-12-04 Daniel Jacobson , Stephen Whitelam

We study an open discrete-time queueing network that models the collection of data in a multi-hop sensor network. We assume data is generated at the sensor nodes as a discrete-time Bernoulli process. All nodes in the network maintain a…

Networking and Internet Architecture · Computer Science 2019-07-26 Iqra Altaf Gillani , Amitabha Bagchi , Pooja Vyavahare

We provide a large deviations analysis of deadlock phenomena occurring in distributed systems sharing common resources. In our model transition probabilities of resource allocation and deallocation are time and space dependent. The process…

Probability · Mathematics 2009-11-24 Francis Comets , Francois Delarue , René Schott

We offer a new point of view on the (Modified) Log-Sobolev inequality and lower bounds on the Ricci-curvature in the setting where the dynamics are obtained as the limit of Markov processes. In this setting, the large deviation rate…

Probability · Mathematics 2016-10-03 Richard C. Kraaij

In many experimental situations, a physical system undergoes stochastic evolution which may be described via random maps between two compact spaces. In the current work, we study the applicability of large deviations theory to time-averaged…

Statistical Mechanics · Physics 2015-05-13 Vladimir Y. Chernyak , Michael Chertkov , Sergey V. Malinin , Razvan Teodorescu

We prove pathwise large deviation principles of slow variables in slow-fast systems in the limit of time-scale separation tending to infinity. In the limit regime we consider, the convergence of the slow variable to its deterministic limit…

Probability · Mathematics 2020-11-25 Richard C. Kraaij , Mikola C. Schlottke

In this article, we analyze three classes of time-reversal of a Markov process with Gaussian noise on a manifold. We first unveil a commutativity constraint for the most general of these time-reversals to be well defined. Then we give a…

Statistical Mechanics · Physics 2024-08-09 Jérémy O'Byrne , Michael E. Cates

We study current fluctuations in lattice gases in the hydrodynamic scaling limit. More precisely, we prove a large deviation principle for the empirical current in the symmetric simple exclusion process with rate functional I. We then…

Probability · Mathematics 2015-12-18 L. Bertini , A. De Sole , D. Gabrielli , G. Jona-Lasinio , C. Landim

For strongly positively recurrent countable state Markov shifts, we bound the distance between an invariant measure and the measure of maximal entropy in terms of the difference of their entropies. This extends an earlier result for…

Dynamical Systems · Mathematics 2021-12-03 René Rühr , Omri Sarig

Piecewise Deterministic Markov Processes (PDMPs) are studied in a general framework. First, different constructions are proven to be equivalent. Second, we introduce a coupling between two PDMPs following the same differential flow which…

Probability · Mathematics 2021-08-03 Alain Durmus , Arnaud Guillin , Pierre Monmarché

In this paper, we reveal a general relationship between model simplification and irreversibility based on the model of continuous-time Markov chains with time-scale separation. According to the topological structure of the fast process, we…

Statistical Mechanics · Physics 2016-06-08 Chen Jia