Abstract. 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 empirical type measure and empirical link measure. From the LLDP, we deduce a full large deviation principle for the typed random graph, and the classical Erdos-Renyi graphs, where nc/2 links are inserted at random among ...

We prove a large deviation principle for the largest eigenvalue of Wigner matrices without Gaussian tails, namely such that the distribution tails P(|X1,1| > t) and P(|X1,2| > t) behave like e−bt α and e−atα respectively for some a, b ∈ (0,+∞) and α ∈ (0, 2). The large deviation principle is of speed Nα/2 and with an explicit good rate function depending only on the tail distribution of the ent...

We establish a sample path large deviation principle for sequences of Markov chains arising in game theory and other applications. As the state spaces of these Markov chains are discrete grids in the simplex, our analysis must account for the fact that the processes run on a set with a boundary. A key step in the analysis establishes joint continuity properties of the state-dependent Cramér tra...

Given a sequence of bounded random variables that satisfies a well known mixing condition, it is shown that empirical estimates of the ratefunction for the partial sums process satisfies the large deviation principle in the space of convex functions equipped with the Attouch-Wets topology. As an application, a large deviation principle for estimating the exponent in the tail of the queue-length...

We prove that the large deviation principle holds for a class of processes inspired by semi-Markov additive processes. For the processes we consider, the sojourn times in the phase process need not be independent and identically distributed. Moreover the state selection process need not be independent of the sojourn times. We assume that the phase process takes values in a finite set and that t...

We study the large and moderate deviations for intersection local times generated by, respectively, independent Brownian local times and independent local times of symmetric random walks. Our result in the Brownian case generalizes the large deviation principle achieved in Mansmann (1991) for the L2-norm of Brownian local times, and coincides with the large deviation obtained by Csörgö, Shi and...

A uniform key renewal theorem is deduced from the uniform Blackwell’s renewal theorem. A uniform LDP (large deviation principle) for renewal-reward processes is obtained, and MDP (moderate deviation principle) is deduced under conditions much weaker than existence of exponential moments.

A statistical relaxation phenomenon is studied for a general class of dispersive wave equations of nonlinear Schrödinger-type which govern non-integrable, non-singular dynamics. In a bounded domain the solutions of these equations have been shown numerically to tend in the long-time limit toward a Gibbsian statistical equilibrium state consisting of a ground-state solitary wave on the large sca...