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We establish a large deviation principle for time dependent trajectories (paths) of the empirical density of $N$ particles with long range interactions, for homogeneous systems. This result extends the classical kinetic theory that leads to…

Statistical Mechanics · Physics 2022-01-19 Ouassim Feliachi , Freddy Bouchet

An optical analog of the quantum weak measurement scheme proved to be very useful for the observation of optical beam shifts. Here we adapt the weak value amplification method for the observation of the angular Goos-Hanchen shift. We…

Optics · Physics 2015-06-19 G. Jayaswal , G. Mistura , M. Merano

We study a sequential system of interacting diffusions in which particle $i$ interacts only with its predecessors through the empirical measure $\mu_t^{i-1}$, yielding a directed, non-exchangeable mean-field approximation of a…

Probability · Mathematics 2026-02-03 Zhenfu Wang , Xianliang Zhao

A key optical parameter characterizing the existence of negative refraction in a thin layer of a composite material is the effective refractive index of an equivalent, homogenized layer with the same physical thickness as the initial…

Consider a collection of particles whose state evolution is described through a system of interacting diffusions in which each particle is driven by an independent individual source of noise and also by a small amount of noise that is…

Probability · Mathematics 2021-01-01 Amarjit Budhiraja , Michael Conroy

In this paper, we show that the empirical measure of mean-field model satisfies the large deviation principle with respect to the weak convergence topology or the stronger Wasserstein metric, under the strong exponential integrability…

Probability · Mathematics 2019-02-20 Wei Liu , Liming Wu

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

Weak amplification is a signal enhancement technique which is used to measure tiny changes that otherwise cannot be determined because of technical limitations. It is based on the existence of a special type of interaction which couples a…

Quantum Physics · Physics 2015-06-04 Juan P. Torres , Graciana Puentes , Nathaniel Hermosa , Luis Jose Salazar-Serrano

We investigate the impact of dissipation on weak measurements. While weak measurements have been successful in signal amplification, dissipation can compromise their usefulness. More precisely, we show that in systems with non-degenerate…

Quantum Physics · Physics 2024-05-13 Lorena Ballesteros Ferraz , John Martin , Yves Caudano

We consider large deviations of empirical measures of diffusion processes. In a first part, we present conditions to obtain a large deviations principle (LDP) for a precise class of unbounded functions. This provides an analogue to the…

Probability · Mathematics 2020-09-23 Grégoire Ferré , Gabriel Stoltz

In this paper we prove a weak comparison principle for a reaction-diffusion system without uniqueness of solutions. We apply the abstract results to the Lotka-Volterra system with diffusion, a generalized logistic equation and to a model of…

Dynamical Systems · Mathematics 2012-05-21 José Valero

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

We establish uniqueness for a class of first-order Hamilton-Jacobi equations with Hamiltonians that arise from the large deviations of the empirical measure and empirical flux pair of weakly interacting Markov jump processes. As a corollary…

Probability · Mathematics 2020-09-24 Richard C. Kraaij

We consider a rate control problem for an $N$-particle weakly interacting finite state Markov process. The process models the state evolution of a large collection of particles and allows for multiple particles to change state…

Probability · Mathematics 2016-03-31 Amarjit Budhiraja , Eric Friedlander

The aim of the paper is to establish a large deviation principle (LDP) for the empirical measure of mean-field interacting diffusions in a random environment. The point is to derive such a result once the environment has been frozen…

Probability · Mathematics 2017-03-08 Eric Luçon

We address the long time behaviour of weakly interacting diffusive particle systems on the d-dimensional torus. Our main result is to show that, under certain regularity conditions, the weak error between the empirical distribution of the…

Analysis of PDEs · Mathematics 2025-05-13 François Delarue , Alvin Tse

We study the limiting behaviour of the empirical measure of a system of diffusions interacting through their ranks when the number of diffusions tends to infinity. We prove that the limiting dynamics is given by a McKean-Vlasov evolution…

Probability · Mathematics 2010-08-30 Mykhaylo Shkolnikov

We establish a Sanov type large deviation principle for an ensemble of interacting Brownian rough paths. As application a large deviations for the ($k$-layer, enhanced) empirical measure of weakly interacting diffusions is obtained. This in…

Probability · Mathematics 2019-04-23 Jean-Dominique Deuschel , Peter K. Friz , Mario Maurelli , Martin Slowik

Weak values are traditionally obtained using a weak interaction between the measured system and a pointer state. It has, however, been pointed out that weak coupling can be replaced by a carefully tailored strong interaction. This paper…

Quantum Physics · Physics 2020-06-24 Jan Roik , Karel Lemr , Antonín Černoch , Karol Bartkiewicz

We prove the large deviation principle for the trajectory of a broad class of mean field interacting Markov jump processes via a general analytic approach based on viscosity solutions. Examples include generalized Ehrenfest models as well…

Probability · Mathematics 2016-06-24 Richard Kraaij