Deviation Principle For Empirical Measures Research Articles

Large deviation principle for empirical measures of multitype random networks

In this article, we study the stochastic block model also known as the multi-type random networks (MRNs). For the stochastic block model or the MRNs, we define the empirical group measure, empirical cooperative measure and the empirical locality measure. We prove joint large deviation principles for these empirical measures of the stochastic block model in the weak topology. These results will form the basis of understanding the asymptotics of the evolutionary and co-evolutionary processes on the stochastic block model.

A large deviation principle for empirical measures on Polish spaces: Application to singular Gibbs measures on manifolds

On montre un principe de grandes déviations pour une suite de processus ponctuels définis par des mesures de probabilités de Gibbs dans un espace polonais. Il est obtenu comme conséquence d’un principe de Laplace pour des mesures de Gibbs non normalisées. On considère quatre applications: Des mesures de Gibbs conditionnées dans des espaces compacts, des gaz de Coulomb sur des variétés riemanniennes compactes, les mesures de Gibbs habituelles sur l’espace euclidien et les zéros des polynômes aléatoires gaussiens. Finalement, on étudie la généralisation des points Fekete et on prouve une version déterministe du principe de Laplace appelée $\Gamma$-convergence. Notre approche est partiellement inspirée par les travaux de Dupuis et ses coauteurs. C’est notablement naturelle et générale en comparaison avec les stratégies habituelles pour les mesures de Gibbs singulières.

Large deviations for empirical measures of switching diffusion processes with small parameters

We consider the asymptotic property of the diffusion processes with Markovian switching. For a general case, we prove a large deviation principle for empirical measures of switching diffusion processes with small parameters.

Spectral Potential, Kullback Action, and Large Deviations of Empirical Measures on Measurable Spaces

In the paper we prove the well-known large deviation principle for empirical measures in the case when independent identically distributed random variables take values in a measurable space instead of a topological space. The domain of the Kullback--Leibler information function is extended in such a way that the McMillan--Breiman theorem becomes a particular case of the large deviation principle.

Large deviation principles for empirical measures of colored random graphs

For any finite colored graph we define the empirical neighborhood measure, which counts the number of vertices of a given color connected to a given number of vertices of each color, and the empirical pair measure, which counts the number of edges connecting each pair of colors. For a class of models of sparse colored random graphs, we prove large deviation principles for these empirical measures in the weak topology. The rate functions governing our large deviation principles can be expressed explicitly in terms of relative entropies. We derive a large deviation principle for the degree distribution of Erd\H{o}s--R\'{e}nyi graphs near criticality.

Large deviation principle for empirical measures generated by Cox point processes

Consider a sequence (Mn) 1=1 of random measures on (0;1) such that (Mn=n) 1=1 satises the large deviation principle with a certain rate function I. Further, letNn be the Cox point process (doubly stochastic Poisson point process) directed byMn. The purpose of this paper is to establish the large deviation principle for the sequence of empirical measures (Nn=n) 1=1 with rate function expressed in terms of I.