Related papers: Large deviations of empirical measures under symme…

We prove a large deviation principle for the point process associated to $k$-element connected components in $\mathbb R^d$ with respect to the connectivity radii $r_n\to\infty$. The random points are generated from a homogeneous Poisson…

The term moderate deviations is often used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between a convergence in probability of some random variables to a constant and a weak convergence…

Let $A$ be a transition probability kernel on a finite state space $\Delta^o =\{1, \ldots , d\}$ such that $A(x,y)>0$ for all $x,y \in \Delta^o$. Consider a reinforced chain given as a sequence $\{X_n, \; n \in \mathbb{N}_0\}$ of…

We consider (annealed) large deviation principles for component empirical measures of several families of marked sparse random graphs, including (i) uniform graphs on $n$ vertices with a fixed degree distribution; (ii) uniform graphs on $n$…

We study the large deviation function for the empirical measure of diffusing particles at one fixed position. We find that the large deviation function exhibits anomalous system size dependence in systems that satisfy the following…

This paper concerns the large deviations of a system of interacting particles on a random graph. There is no stochasticity, and the only sources of disorder are the random graph connections, and the initial condition. The average number of…

We prove a Large Deviation Principle for the random spec- tral measure associated to the pair $(H_N; e)$ where $H_N$ is sampled in the GUE(N) and e is a fixed unit vector (and more generally in the $\beta$- extension of this model). The…

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…

In this article for a finite typed random geometric graph we define the empirical locality distribution, which records the number of nodes of a given type linked to a given number of nodes of each type. We find large deviation principle…

In this article, we prove a joint large deviation principle in $n$ for the \emph{empirical pair measure} and \emph{ empirical offspring measure} of critical multitype Galton-Watson trees conditioned to have exactly $n$ vertices in the weak…

We obtain error rates for large deviations of sums of i.i.d. random variables in, a particular case, of the domain of a non-symmetric infinite mean $\alpha=1$-stable law. The focus of this work is on the method of proof via analytic…

We consider large deviations of empirical measures of diffusion processes. In a first part, we present conditions to obtain a large deviations principle (LDP) for a precise class of unbounded functions. This provides an analogue to the…

We propose a "decomposition method" to prove non-asymptotic bound for the convergence of empirical measures in various dual norms. The main point is to show that if one measures convergence in duality with sufficiently regular observables,…

We consider a two-dimensional Hamiltonian system perturbed by a small diffusion term, whose coefficient is state-dependent and non-degenerate. As a result, the process consists of the fast motion along the level curves and slow motion…

We present large deviations principles for the moments of the empirical spectral measure of Wigner matrices and empirical measure of $\beta$-ensembles in three cases : the case of Wigner matrices without Gaussian tails, that is Wigner…

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…

We consider a class of continuous time Markov chains on a compact metric space that admit an invariant measure strictly positive on open sets together with absorbing states. We prove the joint large deviation principle for the empirical…

We prove large deviation principles for the distribution of the empirical measure of the eigenvalues of Lax matrices following the Generalized Gibbs ensembles of the classical Toda chain introduced in [10]. We deduce the almost sure…

We consider discrete time Markov chains with Polish state space. The large deviations principle for empirical measures of a Markov chain can equivalently be stated in Laplace principle form, which builds on the convex dual pair of relative…

We establish a large deviation theorem for the empirical spectral distribution of random covariance matrices whose entries are independent random variables with mean 0, variance 1 and having controlled forth moments. Some new properties of…