Related papers: Large deviations for empirical entropies of Gibbsi…
The Gibbs entropy of a microcanonical network ensemble is the logarithm of the number of network configurations compatible with a set of hard constraints. This quantity characterizes the level of order and randomness encoded in features of…
In this article, we prove a local large deviation principle (LLDP) for the empirical locality measure of typed random networks on $n$ nodes conditioned to have a given \emph{ empirical type measure} and \emph{ empirical link measure.} From…
We study the problem of estimating a distribution over a finite alphabet from an i.i.d. sample, with accuracy measured in relative entropy (Kullback-Leibler divergence). While optimal bounds on the expected risk are known, high-probability…
We give two examples of periodic Gaussian processes, having entropy numbers of exactly same order but radically different small deviations. Our construction is based on classical Knopp's result yielding of existence of continuous nowhere…
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.}…
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…
Let $K = \{0,1,...,q-1\}$. We use a special class of translation invariant measures on $K^\mathbb{Z}$ called algebraic measures to study the entropy rate of a hidden Markov processes. Under some irreducibility assumptions of the Markov…
We give new and explicitly computable examples of Gibbs-non-Gibbs transitions of mean-field type, using the large deviation approach introduced in [4]. These examples include Brownian motion with small variance and related diffusion…
We consider the task of deriving a key with high HILL entropy from an unpredictable source. Previous to this work, the only known way to transform unpredictability into a key that was $\eps$ indistinguishable from having min-entropy was via…
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…
Bounds on the entropy of patterns of sequences generated by independently identically distributed (i.i.d.) sources are derived. A pattern is a sequence of indices that contains all consecutive integer indices in increasing order of first…
The definition of $k^{th}$-order empirical entropy of strings is extended to node labelled binary trees. A suitable binary encoding of tree straight-line programs (that have been used for grammar-based tree compression before) is shown to…
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 consider the general branching random walk under minimal assumptions, which in particular guarantee that the empirical particle distribution admits an almost sure central limit theorem. For such a process, we study the large time decay…
We establish the Level-1 and Level-3 Large Deviation Principles (LDPs) for invariant measures on shift spaces over finite alphabets under very general decoupling conditions for which the thermodynamic formalism does not apply. Such…
In this paper we study empirical measures which can be thought as a decoupled version of the empirical measures generated by random matrices. We prove the large deviation principle with the rate function, which is finite only on product…
The main results in this paper concern large deviations for families of non-Gaussian processes obtained as suitable perturbations of continuous centered multivariate Gaussian processes which satisfy a large deviation principle. We present…
In this document, we aim to gather various results related to a compositional/categorical approach to rigorous Statistical Mechanics. Rigorous Statistical Mechanics is centered on the mathematical study of statistical systems. Central…
We introduce a family of scale-invariant entropy statistics derived from logarithmically aggregated distance distributions of point processes, with prime numbers serving as a motivating example. The construction associates to each finite…
We consider two Ito equations that evolve on different time scales. The equations are fully coupled in the sense that all coefficients may depend on both the "slow" and the "fast" processes and the diffusion terms may be correlated. The…