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Let $\mathcal{G}(N,\frac 1Nt_N)$ be the Erd\H{o}s-R\'enyi graph with connection probability $\frac 1Nt_N\sim t/N$ as $N\to\infty$ for a fixed $t\in(0,\infty)$. We derive a large-deviations principle for the empirical measure of the sizes of…

Probability · Mathematics 2021-04-26 Luisa Andreis , Wolfgang König , Robert I. A. Patterson

A large deviations principle is established for the joint law of the empirical measure and the flow measure of a renewal Markov process on a finite graph. We do not assume any bound on the arrival times, allowing heavy tailed distributions.…

Probability · Mathematics 2014-02-18 Mauro Mariani , Lorenzo Zambotti

We consider a family of positive operator valued measures associated with representations of compact connected Lie groups. For many independent copies of a single state and a tensor power representation we show that the observed probability…

Mathematical Physics · Physics 2024-09-04 Alonso Botero , Matthias Christandl , Péter Vrana

We show some level-2 large deviation principles for rational maps satisfying a strong form of non-uniform hyperbolicity, called "Topological Collet-Eckmann". More precisely, we prove a large deviation principle for the distribution of…

Dynamical Systems · Mathematics 2015-12-04 Henri Comman , Juan Rivera-Letelier

Large deviation functions are an essential tool in the statistics of rare events. Often they can be obtained by contraction from a so-called level 2 large deviation {\em functional} characterizing the empirical density of the underlying…

Statistical Mechanics · Physics 2016-08-24 Johannes Hoppenau , Daniel Nickelsen , Andreas Engel

Large deviations principle is obtained for terminating multidimensional compound renewal processes. We also obtained the asymptotic of large deviations for the case when a Gibbs change of the original probability measure takes place. The…

Probability · Mathematics 2021-12-20 A. Logachov , A. Mogulskii , E. Prokopenko

For a dynamical system, we study the set of points $\cal W$ whose orbit approximates any chosen point at certain specified rates. Our basic setting is that of left shift acting on topological Markov chains endowed with a local weak Gibbs…

Dynamical Systems · Mathematics 2016-06-09 María Victoria Melián Pérez

The large deviation principle is proved for a class of $L^2$-valued processes that arise from the coarse-graining of a random field. Coarse-grained processes of this kind form the basis of the analysis of local mean-field models in…

Mathematical Physics · Physics 2007-05-23 R. S. Ellis , K. Haven , B. Turkington

Localized sufficient conditions for the large deviation principle of the given stochastic differential equations will be presented for stochastic differential equations with non-Lipschitzian and time-inhomogeneous coefficients, which is…

Probability · Mathematics 2014-04-08 Yunjiao Hu , Guangqiang Lan

The large deviations properties of trajectory observables for chaotic non-invertible deterministic maps as studied recently by N. R. Smith, Phys. Rev. E 106, L042202 (2022) and by R. Gutierrez, A. Canella-Ortiz, C. Perez-Espigares,…

Statistical Mechanics · Physics 2024-01-30 Cecile Monthus

We prove a large deviations principle for the empirical law of the block sizes of a uniformly distributed non-crossing partition. As an application we obtain a variational formula for the maximum of the support of a compactly supported…

Probability · Mathematics 2011-07-04 Janosch Ortmann

We give necessary and sufficient conditions for laws of large numbers to hold in $L^2$ for the empirical measure of a large class of branching Markov processes, including $\lambda$-positive systems but also some $\lambda$-transient ones,…

Probability · Mathematics 2017-11-16 Matthieu Jonckheere , Santiago Saglietti

We establish the weak large deviations principle for empirical measures of Markov chains on $\mathbb R^d$ under mild assumptions. In particular, no irreducibility is assumed and the initial measure may be arbitrary. The proof is entirely…

Probability · Mathematics 2026-04-24 Léo Daures

In this paper we extend the results of Lenci and Rey-Bellet on the large deviation upper bound of the distribution measures of local Hamiltonians with respect to a Gibbs state, in the setting of translation-invariant finite-range…

Mathematical Physics · Physics 2009-11-13 Fumio Hiai , Milan Mosonyi , Tomohiro Ogawa

The Large Deviation Principle is established for stochastic models defined by past-dependent non linear recursions with small noise. In the Markov case we use the result to obtain an explicit expression for the asymptotics of exit time.

Probability · Mathematics 2007-05-23 F. Klebaner , R. Liptser

We establish a large deviation principle for the empirical measure process associated with a general class of finite-state mean field interacting particle systems with Lipschitz continuous transition rates that satisfy a certain ergodicity…

Probability · Mathematics 2016-01-26 Paul Dupuis , Kavita Ramanan , Wei Wu

This paper focuses on systems of nonlinear second-order stochastic differential equations with multi-scales. The motivation for our study stems from mathematical physics and statistical mechanics, for examples, Langevin dynamics and…

Probability · Mathematics 2024-04-08 Nhu N. Nguyen , George Yin

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

We establish a sharp large deviation principle for renewal-reward processes, supposing that each renewal involves a broad-sense reward taking values in a real separable Banach space. In fact, we demonstrate a weak large deviation principle…

Probability · Mathematics 2023-04-24 Marco Zamparo

The purpose of this paper is to ensure the conditions of G\"artner-Ellis Theorem for evaluations of the empirical measure. We show that up-to-date conditions for ensuring the convergence to a quasi-stationary distribution can be applied…

Probability · Mathematics 2020-04-21 Aurélien Velleret