English
Related papers

Related papers: Large Deviations for Empirical Measures of Self-In…

200 papers

We study the large deviations of Markov chains under the sole assumption that the state space is discrete. In particular, we do not require any of the usual irreducibility and exponential tightness assumptions. Using subadditive arguments,…

Probability · Mathematics 2026-05-15 Léo Daures

We consider a class of particle systems described by differential equations (both stochastic and deterministic), in which the interaction network is determined by the realization of an Erd\H{o}s-R\'enyi graph with parameter $p_n\in (0, 1]$,…

Probability · Mathematics 2019-08-06 Fabio Coppini , Helge Dietert , Giambattista Giacomin

The theory of stochastic approximations form the theoretical foundation for studying convergence properties of many popular recursive learning algorithms in statistics, machine learning and statistical physics. Large deviations for…

Probability · Mathematics 2025-02-05 Henrik Hult , Adam Lindhe , Pierre Nyquist , Guo-Jhen Wu

In this article we establish a large deviation principle for the empirical measures of a simple spatially inhomogeneous random walk on $\overline{\mathbb{Z}}$, the two-point compactification of $\mathbb{Z}$. The classical Donsker--Varadhan…

Probability · Mathematics 2026-05-27 Jan-Luka Fatras

We study the large deviation behaviour of the trajectories of empirical distributions of independent copies of time-homogeneous Feller processes on locally compact metric spaces. Under the condition that we can find a suitable core for the…

Functional Analysis · Mathematics 2018-03-13 Richard C. Kraaij

This article examines large time behaviour of finite state mean-field interacting particle systems. Our first main result is a sharp estimate (in the exponential scale) on the time required for convergence of the empirical measure process…

Probability · Mathematics 2021-03-02 Sarath Yasodharan , Rajesh Sundaresan

In this article, we prove a joint large deviation principle in $n$ for the \emph{empirical pair measure} and \emph{ empirical offspring measure} of critical multitype Galton-Watson trees conditioned to have exactly $n$ vertices in the weak…

Probability · Mathematics 2017-08-15 Kwabena Doku-Amponsah

In this paper we consider the statistics of repeated measurements on the output of a quantum Markov chain. We establish a large deviations result analogous to Sanov's theorem for the empirical measure associated to finite sequences of…

Quantum Physics · Physics 2015-06-22 Merlijn van Horssen , Madalin Guta

In order to sample from a given target distribution (often of Gibbs type), the Monte Carlo Markov chain method consists in constructing an ergodic Markov process whose invariant measure is the target distribution. By sampling the Markov…

Probability · Mathematics 2015-06-11 Luc Rey-Bellet , Kostantinos Spiliopoulos

We prove a large deviation principle on path space for a class of discrete time Markov processes whose state space is the intersection of a regular domain $\L\subset \R^d$ with some lattice of spacing $\e$. Transitions from $x$ to $y$ are…

Probability · Mathematics 2007-05-23 Anton Bovier , Veronique Gayrard

We recover the Donsker-Varadhan large deviations principle (LDP) for the empirical measure of a continuous time Markov chain on a countable (finite or infinite) state space from the joint LDP for the empirical measure and the empirical flow…

Probability · Mathematics 2013-01-01 L. Bertini , A. Faggionato , D. Gabrielli

This paper studies large deviations of a ``fully coupled" finite state mean-field interacting particle system in a fast varying environment. The empirical measure of the particles evolves in the slow time scale and the random environment…

Probability · Mathematics 2021-06-24 Sarath Yasodharan , Rajesh Sundaresan

A $\delta$ once-reinforced random walk ($\delta$-ORRW) on connected graph is a self-interacting random walk which moves to its neighbors at each step according to the weights of the edges at that time, where the weights are $1$ on edges…

Probability · Mathematics 2026-03-30 Xiangyu Huang , Yong Liu , Kainan Xiang

We consider a system of $N^{d}$ spins in random environment with a random local mean field type interaction. Each spin has a fixed spatial position on the torus $\mathbb{T}^{d}$, an attached random environment and a spin value in…

Probability · Mathematics 2016-02-05 Patrick E. Müller

We consider particle systems with mean-field interactions whose distribution is invariant by translations. Under the assumption that the system seen from its centre of mass be reversible with respect to a Gibbs measure, we establish large…

Probability · Mathematics 2019-04-25 Julien Reygner

We analyse dynamical large deviations of quantum trajectories in Markovian open quantum systems in their full generality. We derive a {\em quantum level-2.5 large deviation principle} for these systems, which describes the joint…

Statistical Mechanics · Physics 2019-04-10 Federico Carollo , Robert L. Jack , Juan P. Garrahan

In this work, we study the large deviation properties of random walk in a random environment on $\mathbb{Z}^d$ with $d\geq1$. We start with the quenched case, take the point of view of the particle, and prove the large deviation principle…

Probability · Mathematics 2008-09-09 Atilla Yilmaz

The study of chaotic systems, where rare events play a pivotal role, is essential for understanding complex dynamics due to their sensitivity to initial conditions. Recently, tools from large deviation theory, typically applied in the…

Chaotic Dynamics · Physics 2026-05-06 Lucianno Defaveri , Naftali R. Smith

As an important tool characterizing the long time behavior of Markov processes, the Donsker-Varadhan LDP (large deviation principle) does not directly apply to distribution dependent SDEs/SPDEs since the solutions are non-Markovian. We…

Probability · Mathematics 2020-02-21 Panpan Ren , Feng-Yu Wang

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