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A rigorous connection between large deviations theory and Gamma-convergence is established. Applications include representations formulas for rate functions, a contraction principle for measurable maps, a large deviations principle for…

Probability · Mathematics 2018-02-02 Mauro Mariani

We study current fluctuations in lattice gases in the macroscopic limit extending the dynamic approach for density fluctuations developed in previous articles. More precisely, we establish a large deviation principle for a space-time…

Statistical Mechanics · Physics 2015-12-18 L. Bertini , A. De Sole , D. Gabrielli , G. Jona-Lasinio , C. Landim

The chaotic hypothesis has several implications which have generated interest in the literature because of their generality and because a few exact predictions are among them. However its application to Physics problems requires attention…

Statistical Mechanics · Physics 2009-11-11 F. Bonetto , G. Gallavotti , A. Giuliani , F. Zamponi

Considering Langevin dynamics we derive the general form of the stochastic differential that satisfies the Gallavotti-Cohen symmetry. This extends the work previously done by Kurchan, and Lebowitz and Spohn on such systems, and we treat…

Statistical Mechanics · Physics 2007-05-23 Martin Depken

We study a class of dissipative PDE's perturbed by an unbounded kick force. Under some natural assumptions, the restrictions of solutions to integer times form a homogeneous Markov process. Assuming that the noise is rough with respect to…

Mathematical Physics · Physics 2014-10-20 Vojkan Jaksic , Vahagn Nersesyan , Claude-Alain Pillet , Armen Shirikyan

Fluctuation theorems have a very special place in the study of non equilibrium dynamics of physical systems. The form in which it is used most extensively is the Gallavoti-Cohen Fluctuation Theorem which is in terms of the distribution of…

Classical Physics · Physics 2015-12-01 G. S. Agarwal , Sushanta Dattagupta

An effective characterization of chaotic conservative Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor derived from the structure of the Hamiltonian has been extended to a wide class of potential…

Chaotic Dynamics · Physics 2015-05-18 Yossi Ben Zion , Lawrence Horwitz

We use a weak Gibbs property and a weak form of specification to derive level-2 large deviations principles for symbolic systems equipped with a large class of reference measures. This has applications to a broad class of symbolic systems,…

Dynamical Systems · Mathematics 2017-10-25 Vaughn Climenhaga , Daniel J. Thompson , Kenichiro Yamamoto

For a system of globally coupled chaotic maps with bistable behaviour we relate the rate function for large deviations in the system size at finite time to dynamical properties of the self consistent Perron-Frobenius operator (SCPFO) that…

Dynamical Systems · Mathematics 2010-09-09 Gerhard Keller

We consider, for a diffusion process in R^n, the Gallavotti-Cohen functional, defined as the empirical power dissipated in a time interval by the non-conservative part of the drift. We prove a large deviation principle in the limit in which…

Probability · Mathematics 2010-04-15 Lorenzo Bertini , Giacomo Di Gesù

For axiom A diffeomorphisms and equilibrium state, we prove a Large deviation result for the sequence of successive return times into a fixed open set, under some assumption on the boundary. Our result relies on and extends the work by…

Dynamical Systems · Mathematics 2007-09-04 Renaud Leplaideur , Benoît Saussol

The dynamics of many important high-dimensional dynamical systems are both chaotic and complex, meaning that strong reducing hypotheses are required to understand the dynamics. The highly influential chaotic hypothesis of Gallavotti and…

Chaotic Dynamics · Physics 2022-02-04 Caroline L. Wormell

The theory of large deviations deals with the probabilities of rare events (or fluctuations) that are exponentially small as a function of some parameter, e.g., the number of random components of a system, the time over which a stochastic…

Statistical Mechanics · Physics 2012-03-01 Hugo Touchette

In a vast area of probabilistic limit theorems for dynamical systems with chaotic behaviors always only functional form (exponential, power, etc) of the asymptotic laws and of convergence rates were studied. However, for basically all…

Dynamical Systems · Mathematics 2023-06-28 Leonid A. Bunimovich , Yaofeng Su

We establish the Level-1 and Level-3 Large Deviation Principles (LDPs) for invariant measures on shift spaces over finite alphabets under very general decoupling conditions for which the thermodynamic formalism does not apply. Such…

Mathematical Physics · Physics 2019-06-28 Noé Cuneo , Vojkan Jakšić , Claude-Alain Pillet , Armen Shirikyan

Large deviations in chaotic dynamics have potentially significant and dramatic consequences. We study large deviations of series of finite lengths $N$ generated by chaotic maps. The distributions generally display an exponential decay with…

Chaotic Dynamics · Physics 2022-10-21 Naftali R. Smith

We consider a general d-dimensional quantum system of non-interacting particles, with suitable statistics, in a very large (formally infinite) container. We prove that, in equilibrium, the fluctuations in the density of particles in a…

Mathematical Physics · Physics 2007-05-23 Joel L. Lebowitz , Marco Lenci , Herbert Spohn

This work establishes a large deviation principle for the spectral measure of the Lax matrix associated to the periodic Toda chain of $N$ particles, subject to a generalised Gibbs measure. This large deviation principle is governed by a…

Probability · Mathematics 2026-04-08 Tamara Grava , Alice Guionnet , Karol K. Kozlowski , Alex Little

We derive a large deviation principle for families of random variables in the basin of attraction of spectrally positive stable distributions by proving a uniform version of the Tauberian theorem for Laplace-Stieltjes transforms. The main…

Probability · Mathematics 2026-05-25 Giampaolo Cristadoro , Gaia Pozzoli

The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as…

Statistical Mechanics · Physics 2009-08-20 Hugo Touchette