Related papers: Local Large Deviations: McMillian Theorem for mult…

In this work we determine a process-level Large Deviation Principle (LDP) for a model of interacting particles indexed by a lattice $\mathbb{Z}^d$. The connections are random, sparse and unscaled, so that the system converges in the large…

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…

The meaning of thermodynamic descriptions is found in large-deviations scaling of the fluctuations probabilities. The primary large-deviations rate function is the entropy, which is the basis for both fluctuation theorems and for…

We establish a large deviation principle for the solutions of a class of stochastic partial differential equations with non-Lipschitz continuous coefficients. As an application, the large deviation principle is derived for super-Brownian…

Under scenario of high frequency data, consistent estimator of realized Laplace transform of volatility is proposed by \citet{TT2012a} and related central limit theorem has been well established. In this paper, we investigate the asymptotic…

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…

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…

Consider the critical Galton-Watson branching system with infinite variance of the offspring law. We provide an alternative arguments against what Slack~{\cite{Slack68}} did when it seeked for a local expression in the neighborhood of point…

For simplest colored branching processes we prove an analog to the McMillan theorem and calculate Hausdorff dimensions of random fractals defined in terms of the limit behavior of empirical measures generated by finite genetic lines. In…

This paper introduces a framework based on Large Deviation Theory (LDT) to accurately and efficiently compute the rare probabilities of voltage collapse. We formulate the problem as finding the most probable failure point (the instanton) on…

We establish the well-posedness of stationary solutions for a class of SPDEs with locally monotone coefficients, and prove the Freidlin--Wentzell large deviation principle (LDP) for these stationary solutions. The LDP for the associated…

We establish a large deviation principle for the process of the largest eigenvalue of an Hermitian Brownian motion. By a contraction principle, we recover the LDP for the largest eigenvalue of a rank one deformation of the GUE.

We prove pathwise large deviation principles of slow variables in slow-fast systems in the limit of time-scale separation tending to infinity. In the limit regime we consider, the convergence of the slow variable to its deterministic limit…

Fluctuation theorem is one of the major achievements in the field of nonequilibrium statistical mechanics during the past two decades. Steady-state fluctuation theorem of sample entropy production rate in terms of large deviation principle…

Model Predictive Path Integral (MPPI) control is a widely used sampling-based method for trajectory optimization, yet its convergence properties remain only partially understood. This paper provides a direct convergence analysis using…

When analysing statistical systems or stochastic processes, it is often interesting to ask how they behave given that some observable takes some prescribed value. This conditioning problem is well understood within the linear operator…

This paper explores the equivalences between four definitions of uniform large deviations principles and uniform Laplace principles found in the literature. Counterexamples are presented to illustrate the differences between these…

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…

For parabolic stochastic partial differential equations (SPDEs), we show that the numerical methods, including the spatial spectral Galerkin method and further the full discretization via the temporal accelerated exponential Euler method,…

In this paper, we focus on two kinds of large deviations principles (LDPs) of the invariant measures of Langevin equations and their numerical methods, as the noise intensity $\epsilon\to 0$ and the dissipation intensity $\nu\to\infty$…