Related papers: Large deviations of empirical measures under symme…
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…
In order to sample from a given target distribution (often of Gibbs type), the Monte Carlo Markov chain method consists in constructing an ergodic Markov process whose invariant measure is the target distribution. By sampling the Markov…
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 obtain the posterior distribution of a random process conditioned on observing the empirical frequencies of a finite sample path. We find under a rather broad assumption on the "dependence structure" of the process, {\em c.f.}…
The present work provides an original framework for random matrix analysis based on revisiting the concentration of measure theory from a probabilistic point of view. By providing various notions of vector concentration ($q$-exponential,…
Let L be a positive line bundle over a projective complex manifold X. Consider the space of holomorphic sections of the tensor power of order p of L. The determinant of a basis of this space, together with some given probability measure on…
Following our previous work on copula-based nonsymmetric dependence measures, we introduce similar measures for discrete random variables. The measures cover the range between two extremes: independence and complete dependence, which take…
In this short note we consider semi-Markov processes satisfying the condition of direction-time independence (Markov renewal processes). We derive large deviation principles and fluctuation theorems for the empirical current and the…
We establish a large deviation principle for the empirical spectral measure of a sample covariance matrix with sub-Gaussian entries, which extends Bordenave and Caputo's result for Wigner matrices having the same type of entries [7]. To…
We present a large deviation property for the pattern statistics representing the number of occurrences of a symbol in words of given length generated at random according to a rational stochastic model. The result is obtained assuming that…
We establish large deviation principles for the largest eigenvalue of large random matrices with variance profiles. For $N \in \mathbb N$, we consider random $N \times N$ symmetric matrices $H^N$ which are such that…
In this paper we prove a large deviation principle (LDP) for the empirical measure of a general system of mean-field interacting diffusions with singular drift (as the number of particles tends to infinity) and show convergence to the…
We investigate the behavior of the empirical neighbourhood distribution of marked graphs in the framework of local weak convergence. We establish a large deviation principle for such families of empirical measures. The proof builds on…
The entropy of an ergodic finite-alphabet process can be computed from a single typical sample path x_1^n using the entropy of the k-block empirical probability and letting k grow with $n$ roughly like log n. We further assume that the…
We prove large deviation principles (LDPs) for random matrices in the orthogonal group and Stiefel manifold, determining both the speed and good convex rate functions that are explicitly given in terms of certain log-determinants of…
We show the existence of Lebesgue-equivalent conservative and ergodic $\sigma$-finite invariant measures for a wide class of one-dimensional random maps consisting of piecewise convex maps. We also estimate the size of invariant measures…
A rigorous connection between large deviations theory and Gamma-convergence is established. Applications include representations formulas for rate functions, a contraction principle for measurable maps, a large deviations principle for…
The angular measure on the unit sphere characterizes the first-order dependence structure of the components of a random vector in extreme regions and is defined in terms of standardized margins. Its statistical recovery is an important step…
Focusing on stochastic systems arising in mean-field models, the systems under consideration belong to the class of switching diffusions, in which continuous dynamics and discrete events coexist and interact. The discrete events are modeled…
We propose three measures of mutual dependence between multiple random vectors. All the measures are zero if and only if the random vectors are mutually independent. The first measure generalizes distance covariance from pairwise dependence…