Related papers: An almost sure large deviation principle for the H…

We propose a family of "exactly solvable" probability distributions to approximate partition functions of two-dimensional statistical mechanics models. While these distributions lie strictly outside the mean-field framework, their free…

We establish large deviation principle (LDP) for the family of vector-valued random processes $(X^\epsilon,Y^\epsilon),\epsilon\to 0$ defined as $$ X^\epsilon_t=\frac{1}{\epsilon^\kappa}\int_0^t H(\xi^\epsilon_s,Y^\epsilon_s)ds,…

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…

In this paper we derive a Large Deviation Principle (LDP) for inhomogeneous U/V-statistics of a general order. Using this, we derive a LDP for two types of statistics: random multilinear forms, and number of monochromatic copies of a…

In this paper, we introduce a mathematical apparatus that is relevant for understanding a dynamical system with small random perturbations and coupled with the so-called transmutation process -- where the latter jumps from one mode to…

In this article we establish a large deviation principle for the family {\nu_{\epsilon}:\epsilon \in (0,1)} of distributions of the scaled stochastic processes {P_{-\log\sqrt{\epsilon}}Z_t}_{t\leq 1}, where (Z_t)_{t\in \lbrack 0,1]} is a…

We consider an inhomogeneous Erd\H{o}s-R\'enyi random graph $G_N$ with vertex set $[N] = \{1,\dots,N\}$ for which the pair of vertices $i,j \in [N]$, $i\neq j$, is connected by an edge with probability $r_N(\tfrac{i}{N},\tfrac{j}{N})$,…

The theory of large deviations constitutes a mathematical cornerstone in the foundations of Boltzmann-Gibbs statistical mechanics, based on the additive entropy $S_{BG}=- k_B\sum_{i=1}^W p_i \ln p_i$. Its optimization under appropriate…

We study a system of N particles with logarithmic, Coulomb or Riesz pairwise interactions, confined by an external potential. We examine a microscopic quantity, the tagged empirical field, for which we prove a large deviation principle at…

We introduce the concept of matrix liberation process, a random matrix counterpart of the liberation process in free probability, and prove a large deviation upper bound for its empirical distribution with several properties on its rate…

We study the dynamics of smooth interval maps with non-flat critical points. For every such a map that is topologically exact, we establish the full (level-2) Large Deviation Principle for empirical means. In particular, the Large Deviation…

In this paper, we show that the replica symmetry of the Gibbs measure of spherical spin systems is a property of the eigenvalue spacing at the edge of the interaction matrix. In particular, our interaction matrix has \textbf{two} large…

In this paper we introduce and exploit the real replica approach for a minimal generalization of the Hopfield model, by assuming the learned patterns to be distributed accordingly to a standard unit Gaussian. We consider the high storage…

We establish relations between different characterizations of order in spin glass models. We first prove that the broadening of the replica overlap distribution indicated by a nonzero standard deviation of the replica overlap $R^{1,2}$…

Let $\mathcal{G}(N,\frac 1Nt_N)$ be the Erd\H{o}s-R\'enyi graph with connection probability $\frac 1Nt_N\sim t/N$ as $N\to\infty$ for a fixed $t\in(0,\infty)$. We derive a large-deviations principle for the empirical measure of the sizes of…

In this work, we establish, for a strong Feller process, the large deviation principle for the occupation measure conditioned not to exit a given subregion. The rate function vanishes only at a unique measure, which is the so-called…

In this paper, we obtain almost sure invariance principles with rate of order $n^{1/p}\log^\beta n$, $2< p\le 4$, for sums associated to a sequence of reverse martingale differences. Then, we apply those results to obtain similar…

A generalized-statistics variational principle for source separation is formulated by recourse to Tsallis' entropy subjected to the additive duality and employing constraints described by normal averages. The variational principle is…

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…

Given a sequence of Borel probability measures on a Hausdorff space which satisfy a large deviation principle, we consider the corresponding sequence of measures formed by conditioning on a set $B$. If the large deviation rate function $I$…