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Related papers: Nonconventional Large Deviations Theorems

200 papers

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

We prove large and moderate deviation principles for the distribution of an empirical mean conditioned by the value of the sum of discrete i.i.d. random variables. Some applications for combinatoric problems are discussed.

Probability · Mathematics 2007-07-11 Fabrice Gamboa , Thierry Klein , Clémentine Prieur

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

A large deviation principle is established for a general class of stochastic flows in the small noise limit. This result is then applied to a Bayesian formulation of an image matching problem, and an approximate maximum likelihood property…

Statistics Theory · Mathematics 2010-02-24 Amarjit Budhiraja , Paul Dupuis , Vasileios Maroulas

In this paper we propose a framework that enables the study of large deviations for point processes based on stationary sequences with regularly varying tails. This framework allows us to keep track not of the magnitude of the extreme…

Probability · Mathematics 2009-08-21 Henrik Hult , Gennady Samorodnitsky

The paper is a sketch of systematic presentation of distributional limit theorems and their refinements for compound sums. When analyzing, e.g., ergodic semi-Markov systems with discrete or continuous time, this allows us to separate those…

Probability · Mathematics 2024-04-29 Vsevolod K. Malinovskii

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 the framework of Harnack type Dirichlet forms, we prove a large deviation principle for the asymptotics of reversible Markov processes with rate function given by the energy of the paths.

Probability · Mathematics 2009-07-28 Ann-Kathrin Jarecki

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

Nonlinear response occurs naturally when a strong perturbation takes a system far from equilibrium. Despite of its omnipresence in nanoscale systems, it is difficult to predict in a general and efficient way. Here we introduce a way to…

Statistical Mechanics · Physics 2019-07-24 Chloe Ya Gao , David T. Limmer

We introduce and test an algorithm that adaptively estimates large deviation functions characterizing the fluctuations of additive functionals of Markov processes in the long-time limit. These functions play an important role for predicting…

Statistical Mechanics · Physics 2023-03-30 Grégoire Ferré , Hugo Touchette

Our aim is to unify and extend the large deviation upper and lower bounds for the occupation times of a Markov process with $L_2$ semigroups under minimal conditions on the state space and the process trajectories; for example, no strong…

Probability · Mathematics 2008-09-24 Naresh Jain , Nicolai Krylov

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 noncommutative analogs of some well-known large deviation inequalities for noncommutative random variables. Firstly, for the noncommutative independent case, we characterize the uniformly exponential integrability of random…

Operator Algebras · Mathematics 2026-04-08 Yong Jiao , Sijie Luo , Dejian Zhou

The link between Tauberian theorems and large deviations is surveyed, with particular reference to regular variation.

Probability · Mathematics 2008-01-03 N. H. Bingham

We present a review of recent work on the statistical mechanics of non equilibrium processes based on the analysis of large deviations properties of microscopic systems. Stochastic lattice gases are non trivial models of such phenomena and…

Probability · Mathematics 2015-12-18 L. Bertini , A. De Sole , D. Gabrielli , G. Jona-Lasinio , C. Landim

We study the large deviations of sums of correlated random variables described by a matrix product ansatz, which generalizes the product structure of independent random variables to matrices whose non-commutativity is the source of…

Statistical Mechanics · Physics 2014-02-18 Florian Angeletti , Hugo Touchette , Eric Bertin , Patrice Abry

Quantum trajectories are Markov processes modeling the evolution of a quantum system subjected to repeated independent measurements. Under purification and irreducibility assumptions, these Markov processes admit a unique invariant measure…

Probability · Mathematics 2023-07-13 Tristan Benoist , Jan-Luka Fatras , Clément Pellegrini

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

For a Markov process associated with a diffusion type Dirichlet form an upper bound is shown for the law of the finite dimensional distributions of the process. Under some more assumptions on the underlaying space this is also shown for the…

Probability · Mathematics 2009-07-28 Ann-Kathrin Jarecki