Related papers: Moderate Deviations for Mean Field Particle Models
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…
Many natural phenomena are effectively described by interacting particle systems, which can be modeled using either deterministic or stochastic differential equations (SDEs). In this study, we specifically investigate particle systems…
We prove two Large deviations principles (LDP) in the zone of moderate deviation probabilities. First we establish LDP for the conditional distributions of moderate deviations of empirical bootstrap measures given empirical probability…
In this paper, we derive the moderate deviation principle for stationary sequences of bounded random variables with values in a Hilbert space. The conditions obtained are expressed in terms of martingale-type conditions. The main tools are…
We consider a stable but nearly unstable autoregressive process of any order. The bridge between stability and instability is expressed by a time-varying companion matrix $A_{n}$ with spectral radius $\rho(A_{n}) < 1$ satisfying…
The purpose of the present paper is to establish moderate deviation principles for a rather general class of random variables fulfilling certain bounds of the cumulants. We apply a celebrated lemma of the theory of large deviations…
In this paper, we establish a large deviations principle (LDP) for interacting particle systems that arise from state and action dynamics of discrete-time mean-field games under the equilibrium policy of the infinite-population limit. The…
We study two interacting particle systems, both modeled as a system of $N$ stochastic differential equations driven by Brownian motions with singular kernels and moderate interaction. We show a quantitative result where the convergence rate…
Motivated by the study of dependent random variables by coupling with independent blocks of variables, we obtain first sufficient conditions for the moderate deviation principle in its functional form for triangular arrays of independent…
Consider a population of individuals belonging to an infinity number of types, and assume that type proportions follow the two-parameter Poisson-Dirichlet distribution. A sample of size n is selected from the population. The total number of…
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…
The Moderate Deviations Principle (MDP) is well-understood for sums of independent random variables, worse understood for stationary random sequences, and scantily understood for random fields. Here it is established for splittable random…
Active systems, which are driven out of equilibrium by local non-conservative forces, exhibit unique behaviors and structures with potential utility for the design of novel materials. An important and difficult challenge along the path…
The aim of this work is to implement a statistical mechanics theory of social interaction, generalizing econometric discrete choice models. A class of simple mean field discrete models is introduced and discussed both from the theoretical…
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…
The term \emph{moderate deviations} is often used in the literature to mean a class of large deviation principles that, in some sense, fill the gap between a convergence in probability to zero (governed by a large deviation principle) and a…
The primitive model describes ions by point charges with an additional hard-core interaction. In classical density-functional theory the mean-field electrostatic contribution can be obtained from the first order of a functional perturbation…
The main aim of this paper is to study the moderate deviation principle for McKean-Vlasov stochastic differential equations with multiple scales. Specifically, we are interested in the asymptotic estimates of the deviation processes…
Importance sampling has become an important tool for the computation of tail-based risk measures. Since such quantities are often determined mainly by rare events standard Monte Carlo can be inefficient and importance sampling provides a…
The purpose of the present paper is to establish explicit bounds on moderate deviation probabilities for a rather general class of geometric functionals enjoying the stabilization property, under Poisson input and the assumption of a…