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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

Much work in the study of large deviations for random graph models is focused on the dense regime where the theory of graphons has emerged as a principal tool. These tools do not give a good approach to large deviation problems for random…

Probability · Mathematics 2020-07-07 Shankar Bhamidi , Amarjit Budhiraja , Paul Dupuis , Ruoyu Wu

We prove a large-deviation principle (LDP) for the sample paths of jump Markov processes in the small noise limit when, possibly, all the jump rates vanish uniformly, but slowly enough, in a region of the state space. We further discuss the…

Probability · Mathematics 2021-02-26 Andrea Agazzi , Luisa Andreis , Robert I. A. Patterson , D. R. Michiel Renger

We consider a system of stochastic interacting particles in $\mathbb{R}^d$ and we describe large deviations asymptotics in a joint mean-field and small-noise limit. Precisely, a large deviations principle (LDP) is established for the…

Probability · Mathematics 2020-11-17 Carlo Orrieri

We consider a sequence of processes defined on half-line for all non negative t. We give sufficient conditions for Large Deviation Principle (LDP) to hold in the space of continuous functions with a new metric that is more sensitive to…

Probability · Mathematics 2015-11-30 F. C. Klebaner , A. V. Logachov , A. A. Mogulski

We prove a Large Deviations Principle (LDP) for systems of diffusions (particles) interacting through their ranks, when the number of particles tends to infinity. We show that the limiting particle density is given by the unique solution of…

Probability · Mathematics 2017-04-05 Amir Dembo , Mykhaylo Shkolnikov , S. R. Srinivasa Varadhan , Ofer Zeitouni

In this work, we study large deviation properties of the covariance process in fully connected Gaussian deep neural networks. More precisely, we establish a large deviation principle (LDP) for the covariance process in a functional…

Probability · Mathematics 2025-05-14 Luisa Andreis , Federico Bassetti , Christian Hirsch

Recently, a number of physical models has emerged described by a random process with increments given by a quadratic form of a fast Gaussian process. We find that the rate function which describes sample-path large deviations for such a…

Statistical Mechanics · Physics 2023-04-25 Freddy Bouchet , Roger Tribe , Oleg Zaboronski

Particle approximations for certain nonlinear and nonlocal reaction-diffusion equations are studied using a system of Brownian motions with killing. The system is described by a collection of i.i.d. Brownian particles where each particle is…

Probability · Mathematics 2019-05-01 Amarjit Budhiraja , Wai-Tong Louis Fan , Ruoyu Wu

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

Fix a smooth Morse function $U\colon \mathbb{R}^{d}\to\mathbb{R}$ with finitely many critical points, and consider the solution of the stochastic differential equation \[ d\boldsymbol{x}_{\epsilon}(t)=-\nabla…

Probability · Mathematics 2025-09-18 Claudio Landim , Jungkyoung Lee , Mauro Mariani

We investigate the large deviation principle (LDP) of the stationary solutions of stochastic functional differential equations (SFDEs) with infinite delay under small random perturbation. First, we demonstrate the existence and uniqueness…

Probability · Mathematics 2026-05-18 Yong Liu , Bin Tang

A large deviation principle is established for a two-scale stochastic system in which the slow component is a continuous process given by a small noise finite dimensional It\^{o} stochastic differential equation, and the fast component is a…

Probability · Mathematics 2017-05-09 Amarjit Budhiraja , Paul Dupuis , Arnab Ganguly

The main goal of this article is to study the effect of small, highly nonlinear, unbounded drifts (small time large deviation principle (LDP) based on exponential equivalence arguments) for a class of stochastic partial differential…

Probability · Mathematics 2022-12-27 Ankit Kumar , Manil T. Mohan

We analytically evaluate the large deviation function in a simple model of classical particle transfer between two reservoirs. We illustrate how the asymptotic large time regime is reached starting from a special propagating initial…

Statistical Mechanics · Physics 2015-06-16 Upendra Harbola , Christian Van den Broeck , Katja Lindenberg

We establish the well-posedness of stationary solutions for a class of SPDEs with locally monotone coefficients, and prove the Freidlin--Wentzell large deviation principle (LDP) for these stationary solutions. The LDP for the associated…

Probability · Mathematics 2026-04-27 Yong Liu , Bin Tang , Rangrang Zhang

Fluctuation theorem is one of the major achievements in the field of nonequilibrium statistical mechanics during the past two decades. Steady-state fluctuation theorem of sample entropy production rate in terms of large deviation principle…

Probability · Mathematics 2016-08-24 Yong Chen , Hao Ge , Jie Xiong , Lihu Xu

We consider a diffusion process on $\mathbb R^n$ and prove a large deviation principle for the empirical process in the joint limit in which the time window diverges and the noise vanishes. The corresponding rate function is given by the…

Probability · Mathematics 2024-12-31 Lorenzo Bertini , Davide Gabrielli , Claudio Landim

We establish, under the Cramer exponential moment condition in a neighbourhood of zero, the Extended Large Deviation Principle for the Random Walk and the Compound Poisson processes in the metric space $\V$ of functions of finite variation…

Probability · Mathematics 2016-11-01 F. C. Klebaner , A. A. Mogulskii

This article concerns the large deviations regime and the consequent solution of the Kramers problem for a two-time scale stochastic system driven by a common jump noise signal perturbed in small intensity $\varepsilon>0$ and with…

Probability · Mathematics 2022-07-15 Pedro Catuogno , André de Oliveira Gomes