Related papers: Large Deviations of a Network of Neurons with Dyna…
In this work we determine a process-level Large Deviation Principle (LDP) for a model of interacting neurons indexed by a lattice $\mathbb{Z}^d$. The neurons are subject to noise, which is modelled as a correlated martingale. The…
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…
We study the large deviation behavior of a system of diffusing particles with a mean field interaction, described through a collection of stochastic differential equations, in which each particle is driven by a vanishing independent…
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…
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…
This paper concerns the large deviations of a system of interacting particles on a random graph. There is no stochasticity, and the only sources of disorder are the random graph connections, and the initial condition. The average number of…
We consider the quasi-deterministic behavior of systems with a large number, $n$, of deterministically interacting constituents. This work extends the results of a previous paper [J. Stat. Phys. 99:1225-1249 (2000)] to include vector-valued…
We prove the Large Deviation Principle for the empirical process in a system of locally interacting Brownian motions in the nonequilibrium dynamic. Such a phenomenon has been proven only for two lattice systems: the symmetric simple…
Using the weak convergence approach to large deviations, we formulate and prove the large deviation principle (LDP) for W-random graphs in the cut-norm topology. This generalizes the LDP for Erd\H{o}s-R{\' e}nyi random graphs by Chatterjee…
We analyze the macroscopic behavior of multi-populations randomly connected neural networks with interaction delays. Similar to cases occurring in spin glasses, we show that the sequences of empirical measures satisfy a large deviation…
In a series of two papers, we investigate the large deviations and asymptotic behavior of stochastic models of brain neural networks with random interaction coefficients. In this first paper, we take into account the spatial structure of…
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…
In this paper we study the Large Deviation Principle (LDP in abbreviation) for a class of Stochastic Partial Differential Equations (SPDEs) in the whole space $\mathbb{R}^d$, with arbitrary dimension $d\geq 1$, under random influence which…
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…
We combine hydrodynamic and modulated energy techniques to study the large deviations of systems of particles with pairwise singular repulsive interactions and additive noise. Specifically, we examine periodic Riesz interactions indexed by…
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…
We study the large deviation principle (LDP) for locally damped nonlinear wave equations perturbed by a bounded noise. When the noise is sufficiently non-degenerate, we establish the LDP for empirical distributions with lower bound of a…
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…
We prove a Large Deviation Principle for {\color{blue} jump-Markov } Processes on sparse large disordered network with disordered connectivity. The network is embedded in a geometric space, with the probability of a connection a (scaled)…
We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit…