Related papers: Convergence to the asymptotic large deviation limi…
We study large deviation asymptotics for processes defined in terms of continued fraction digits. We use the continued fraction digit sum process to define a stopping time and derive a joint large deviation asymptotic for the upper and…
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…
Information thermodynamics provides a framework for studying the effect of feedback loops on entropy production. It has enabled the understanding of novel thermodynamic systems such as the information engine which can be seen as a modern…
This paper is concerned with the general theme of relating the Large Deviation Principle (LDP) for the invariant measures of stochastic processes to the associated sample path LDP. It is shown that if the sample path deviation function…
We study large deviations asymptotics for a class of unbounded additive functionals, interpreted as normalized accumulated areas, of one-dimensional Langevin diffusions with sub-linear gradient drifts. Our results provide parametric…
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…
We study a large deviation principle for a system of stochastic reaction--diffusion equations (SRDEs) with a separation of fast and slow components and small noise in the slow component. The derivation of the large deviation principle is…
Accurate estimation of tail probabilities of projections of high-dimensional probability measures is of relevance in high-dimensional statistics and asymptotic geometric analysis. Whereas large deviation principles identify the asymptotic…
In various disordered systems or non-equilibrium dynamical models, the large deviations of some observables have been found to display different scalings for rare values bigger or smaller than the typical value. In the present paper, we…
We present a complete framework for determining the asymptotic (or logarithmic) efficiency of estimators of large deviation probabilities and rate functions based on importance sampling. The framework relies on the idea that importance…
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…
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…
We give a new proof of the large deviation principle from the hydrodynamic limit for the Ginzberg-Landau model studied in Donsker and Varadhan (1989) using techniques from the theory of stochastic control and weak convergence methods. The…
The standard Large Deviation Theory (LDT) is mathematically illustrated by the Boltzmann-Gibbs factor which describes the thermal equilibrium of short-range-interacting many-body Hamiltonian systems, the velocity distribution of which is…
Time-irreversible stochastic processes are frequently used in natural sciences to explain non-equilibrium phenomena and to design efficient stochastic algorithms. Our main goal in this thesis is to analyse their dynamics by means of large…
The incidence of rare events in fast-slow systems is investigated via analysis of the large deviation principle (LDP) that characterizes the likelihood and pathway of large fluctuations of the slow variables away from their mean behavior --…
Let $\boldsymbol W=\{\boldsymbol W_n:n\in\mathbb N\}$ be a sequence of random vectors in $\mathbb R^d$, $d\ge 1$. This paper considers the logarithmic asymptotics of the extremes of $\boldsymbol W$, that is, for any vector $\boldsymbol…
The purpose of this paper is to ensure the conditions of G\"artner-Ellis Theorem for evaluations of the empirical measure. We show that up-to-date conditions for ensuring the convergence to a quasi-stationary distribution can be applied…
We prove a large deviations principle for the empirical measure of the one dimensional symmetric simple exclusion process in contact with reservoirs. The dynamics of the reservoirs is slowed down with respect to the dynamics of the system,…
This paper introduces novel frameworks for large deviations and metastability analysis in heavy-tailed stochastic dynamical systems. We develop and apply these frameworks within the context of stochastic difference equation $X^\eta_{j+1}(x)…