Related papers: Moderate Deviations for Mean Field Particle Models
Mean field theory is a device to analyze the collective behavior of a dynamical system comprising many interacting particles. The theory allows to reduce the behavior of the system to the properties of a handful of parameters. In neural…
We consider an interacting system of one-dimensional structures modelling fibers with fiber-fiber interaction in a fiber lay-down process. The resulting microscopic system is investigated by looking at different asymptotic limits of the…
We consider particle systems with mean-field interactions whose distribution is invariant by translations. Under the assumption that the system seen from its centre of mass be reversible with respect to a Gibbs measure, we establish large…
Using the hyper-exponential recurrence criterion, a large deviation principle for the occupation measure is derived for a class of non-linear monotone stochastic partial differential equations. The main results are applied to many concrete…
Starting from a microscopic model for a system of neurons evolving in time which individually follow a stochastic integrate-and-fire type model, we study a mean-field limit of the system. Our model is described by a system of SDEs with…
Dynamical Mean-Field Theory (DMFT) has opened new perspectives for the investigation of strongly correlated electron systems and greatly improved our understanding of correlation effects in models and materials. In contrast to…
Static and dynamical aspects of nuclear systems are described through an extended time-dependent mean-field approach. The foundations of the formalism are presented, with highlights on the estimation of average values and their…
We propose a formalism to take account of the correction of the spatial fluctuations to the local self-energy obtained by the dynamical mean-field approximation. For this purpose, the approximate dynamical susceptibility in the framework of…
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…
A broad class of systems, including ecological, epidemiological, and sociological ones, are characterized by populations of individuals assigned to specific categories, e.g., a chemical species, an opinion or an epidemic state, that are…
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…
In this paper we prove large and moderate deviations principles for the recursive kernel estimator of a probability density function and its partial derivatives. Unlike the density estimator, the derivatives estimators exhibit a quadratic…
We modify the Glauber dynamics of the Curie-Weiss model with dissipation in Dai Pra, Fischer, Regoli[2013] by considering arbitrary transition rates and we analyze the phase-portrait as well as the dynamics of moderate fluctuations for…
The main difficulty that arises in the analysis of most machine learning algorithms is to handle, analytically and numerically, a large number of interacting random variables. In this Ph.D manuscript, we revisit an approach based on the…
We study the mean-field limit of a generic class of dynamic co-evolving latent space networks motivated by the social and opinion dynamics literature. Such models include $n$ agents, whose opinions are given by latent stochastic processes,…
We study moderate deviations from hydrodynamic limits of a reaction diffusion model. The process is defined as the superposition of the symmetric exclusion process with a Glauber dynamics. When the process starts from a product measure with…
Dissipation and fluctuations of one-body observables in heavy-ion reactions around the Coulomb barrier are investigated with a microscopic stochastic mean-field approach. By projecting the stochastic mean-field dynamics on a suitable…
In this paper, we study discrete-time absorbing Markov Decision Processes (MDP) with measurable state space and Borel action space with a given initial distribution. For such models, solutions to the characteristic equation that are not…
How do topological defects affect the degree of order in active matter? To answer this question we investigate an agent-based model of self-propelled particles, which accounts for polar alignment and short-ranged repulsive interactions. For…
We study large deviation properties of systems of weakly interacting particles modeled by It\^{o} stochastic differential equations (SDEs). It is known under certain conditions that the corresponding sequence of empirical measures…