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We study the large deviation function for the entropy production rate in two driven one-dimensional systems: the asymmetric random walk on a discrete lattice and Brownian motion in a continuous periodic potential. We compare two approaches:…

Statistical Mechanics · Physics 2013-01-21 Thomas Speck , Andreas Engel , Udo Seifert

We investigate periodic points of the Dyck shift from the viewpoint of large deviations. We establish the level-2 Large Deviation Principle with the rate function given in terms of Kolmogorov-Sinai entropies of shift-invariant Borel…

Dynamical Systems · Mathematics 2025-03-19 Hiroki Takahasi

We consider generalized Bayesian inference on stochastic processes and dynamical systems with potentially long-range dependency. Given a sequence of observations, a class of parametrized model processes with a prior distribution, and a loss…

Statistics Theory · Mathematics 2023-04-26 Langxuan Su , Sayan Mukherjee

The large deviations at various levels that are explicit for Markov jump processes satisfying detailed-balance are revisited in terms of the supersymmetric quantum Hamiltonian $H$ that can be obtained from the Markov generator via a…

Statistical Mechanics · Physics 2024-07-15 Cecile Monthus

Recently the so-called Prabhakar generalization of the fractional Poisson counting process attracted much interest for his flexibility to adapt real world situations. In this renewal process the waiting times between events are IID…

Probability · Mathematics 2020-12-10 Thomas M. Michelitsch , Federico Polito , Alejandro P. Riascos

We propose a computational method for large deviation statistics of time-averaged quantities in general Markov processes. In our proposed method, we repeat a response measurement against external forces, where the forces are determined by…

Statistical Mechanics · Physics 2014-03-12 Takahiro Nemoto , Shin-ichi Sasa

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

Large deviation functions contain information on the stability and response of systems driven into nonequilibrium steady states, and in such a way are similar to free energies for systems at equilibrium. As with equilibrium free energies,…

Statistical Mechanics · Physics 2018-04-25 Ushnish Ray , Garnet Kin-Lic Chan , David T. Limmer

We consider a pure jump process $\{X_t\}_{t\ge 0}$ with values in a finite state space $S= \{1, \ldots, d\}$ for which the jump rates at time instant $t$ depend on the occupation measure $L_t \doteq t^{-1} \int_0^t \delta_{X_s}\,ds$. Such…

Probability · Mathematics 2025-10-17 Amarjit Budhiraja , Francesco Coghi

Markov processes with stochastic resetting towards the origin generically converge towards non-equilibrium steady-states. Long dynamical trajectories can be thus analyzed via the large deviations at Level 2.5 for the joint probability of…

Statistical Mechanics · Physics 2021-05-07 Cecile Monthus

In this paper we prove large deviations principles for the Nadaraya-Watson estimator of the regression of a real-valued variable with a functional covariate. Under suitable conditions, we show pointwise and uniform large deviations theorems…

Statistics Theory · Mathematics 2011-06-15 Mohamed Cherfi

We establish a link between the phenomenon of Taylor dispersion and the theory of empirical distributions. Using this connection, we derive, upon applying the theory of large deviations, an alternative and much more precise description of…

Statistical Mechanics · Physics 2017-02-01 Marcel Kahlen , Andreas Engel , Christian Van den Broeck

We solve two problems related to the fluctuations of time-integrated functionals of Markov diffusions, used in physics to model nonequilibrium systems. In the first we derive and illustrate the appropriate boundary conditions on the…

Statistical Mechanics · Physics 2023-02-01 Johan du Buisson

We introduce a numerical procedure to evaluate directly the probabilities of large deviations of physical quantities, such as current or density, that are local in time. The large-deviation functions are given in terms of the typical…

Statistical Mechanics · Physics 2009-11-11 Cristian Giardina' , Jorge Kurchan , Luca Peliti

Boltzmann-Sanov and Cramer-Chernoff's theorems provide large deviation probabilities, entropy, and rate functions for the spatial distribution of systems and the total internal energy of an ensemble respectively. By the method of Lagrange's…

Statistical Mechanics · Physics 2021-09-17 D. P. Shinde

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 present two examples of a large deviations principle where the rate function is not strictly convex. This is motivated by a model used in mathematical finance (the Heston model), and adds a new item to the zoology of non strictly convex…

Probability · Mathematics 2016-04-19 Stefano De Marco , Antoine Jacquier , Patrick Roome

A basic result of large deviations theory is Sanov's theorem, which states that the sequence of empirical measures of independent and identically distributed samples satisfies the large deviation principle with rate function given by…

Probability · Mathematics 2014-10-17 Markus Fischer

We study the convergence of statistical estimators used in the estimation of large deviation functions describing the fluctuations of equilibrium, nonequilibrium, and manmade stochastic systems. We give conditions for the convergence of…

Statistical Mechanics · Physics 2015-11-09 Christian M. Rohwer , Florian Angeletti , Hugo Touchette

Motivated by the theory of large deviations, we introduce a class of non-negative non-linear functionals that have a variational "rate function" representation.

Probability · Mathematics 2007-05-23 H. Bell , W. Bryc