Related papers: Large Deviation Analysis for Canonical Gibbs Measu…

We study wide Bayesian neural networks focusing on the rare but statistically dominant fluctuations that govern posterior concentration, beyond Gaussian-process limits. Large-deviation theory provides explicit variational objectives-rate…

We show that classical density functional theory can be based on the constrained search method [M. Levy, Proc. Natl. Acad. Sci. 76, 6062 (1979)]. From the Gibbs inequality one first derives a variational principle for the grand potential as…

An integration by parts formula is derived for the first order differential operator corresponding to the action of translations on the space of locally finite simple configurations of infinitely many points on R^d. As reference measures,…

We study a model of spatial random permutations over a discrete set of points. Formally, a permutation $\sigma$ is sampled proportionally to the weight $\exp\{-\alpha \sum_x V(\sigma(x)-x)\},$ where $\alpha>0$ is the temperature and $V$ is…

Thanks to technological advances leading to near-continuous time observations, emerging multivariate point process data offer new opportunities for causal discovery. However, a key obstacle in achieving this goal is that many relevant…

We investigate, in a fairly general setting, the limit of large volume equilibrium Gibbs measures for elasticity type Hamiltonians with clamped boundary conditions. The existence of a quasiconvex free energy, forming the large deviations…

We establish large deviation estimates for Poisson driven models of infectious disease, and apply those estimates to the time of exit from the basin of attraction of an endemic equilibrium. We apply our results to the classical SIRS model.

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…

We consider a general system of n noninteracting identical particles which evolve under a given dynamical law and whose initial microstates are a priori independent. The time evolution of the n-particle average of a bounded function on the…

The theory of large deviations constitutes a mathematical cornerstone in the foundations of Boltzmann-Gibbs statistical mechanics, based on the additive entropy $S_{BG}=- k_B\sum_{i=1}^W p_i \ln p_i$. Its optimization under appropriate…

We consider a jump-diffusion process on a bounded domain with reflection at the boundary, and establish long-term results for a general additive process of its path. This includes the long-term behaviour of its occupation time in the…

We study the large deviations for Cox-Ingersoll-Ross (CIR) processes with small noise and state-dependent fast switching via associated Hamilton-Jacobi equations. As the separation of time scales, when the noise goes to $0$ and the rate of…

We discuss a method to solve models with long-range interactions in the microcanonical and canonical ensemble. The method closely follows the one introduced by Ellis, Physica D 133, 106 (1999), which uses large deviation techniques. We show…

We first study a $d$-dimensional branching Brownian motion (BBM) among mild Poissonian obstacles, where a random trap field in $\mathbb{R}^d$ is created via a Poisson point process. The trap field consists of balls of fixed radius centered…

This paper deals with rare events in a general {interacting gas} at high temperature, by means of Large Deviations Principles. The main result is an LDP for the tagged empirical field, which features the competition of an energy term and an…

Recently, a generalized Bernoulli process (GBP) was developed as a stationary binary sequence whose covariance function obeys a power law. In this paper, we further develop generalized Bernoulli processes, reveal their asymptotic behaviors,…

We study two problems. First, we consider the large deviation behavior of empirical measures of certain diffusion processes as, simultaneously, the time horizon becomes large and noise becomes vanishingly small. The law of large numbers…

This work develops a methodology for analyzing large-deviation lower tails associated with geometric functionals computed on a homogeneous Poisson point process. The technique applies to characteristics expressed in terms of stabilizing…

Gibbs point processes (GPPs) constitute a large and flexible class of spatial point processes with explicit dependence between the points. They can model attractive as well as repulsive point patterns. Feature selection procedures are an…

We establish a Large Deviations Principle for stochastic processes with Lipschitz continuous oblique reflections on regular domains. The rate functional is given as the value function of a control problem and is proved to be good. The proof…