Related papers: Large deviation principles for hypersingular Riesz…
We consider the Gaussian beta-ensemble when $\beta$ scales with $n$ the number of particles such that $\displaystyle{{n}^{-1}\ll \beta\ll 1}$. Under a certain regime for $\beta$, we show that the largest particle satisfies a large…
We consider the $N$ particle classical Riesz gas confined in a one-dimensional external harmonic potential with power law interaction of the form $1/r^k$ where $r$ is the separation between particles. As special limits it contains several…
Let $\Sigma_{A}(\mathbb{N})$ be a topologically mixing countable Markov shift with the BIP property over the alphabet $\mathbb{N}$ and $f: \Sigma_{A}(\mathbb{N}) \rightarrow \mathbb{R}$ a potential satisfying the Walters condition with…
We establish a large deviation principle for time dependent trajectories (paths) of the empirical density of $N$ particles with long range interactions, for homogeneous systems. This result extends the classical kinetic theory that leads to…
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…
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 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 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 prove a large deviation principle for a sequence of point processes defined by Gibbs probability measures on a Polish space. This is obtained as a consequence of a more general Laplace principle for the non-normalized Gibbs measures. We…
We study two one-parameter families of point processes connected to random matrices: the Sine_beta and Sch_tau processes. The first one is the bulk point process limit for the Gaussian beta-ensemble. For beta=1, 2 and 4 it gives the limit…
For a compact $ d $-dimensional rectifiable subset of $ \mathbb{R}^{p} $ we study asymptotic properties as $ N\to\infty $ of $N$-point configurations minimizing the energy arising from a Riesz $ s $-potential $ 1/r^s $ and an external field…
We consider two compact metric spaces $J$ and $X$ and a uniform contractible iterated function system $\{\phi_j: X \to X \, | \, j \in J \}$. For a Lipschitz continuous function $A$ on $J \times X$ and for each $\beta>0$ we consider the…
The Riesz $s$-energy of an $N$-point configuration in the Euclidean space $\mathbb{R}^{p}$ is defined as the sum of reciprocal $s$-powers of all mutual distances in this system. In the limit $s\to0$ the Riesz $s$-potential $1/r^s$ ($r$ the…
This work establishes a large deviation principle for the spectral measure of the Lax matrix associated to the periodic Toda chain of $N$ particles, subject to a generalised Gibbs measure. This large deviation principle is governed by a…
This paper is concerned with the large deviation principle of the stochastic reaction-diffusion lattice systems defined on the N-dimensional integer set, where the nonlinear drift term is locally Lipschitz continuous with polynomial growth…
In this paper, we show that the empirical measure of mean-field model satisfies the large deviation principle with respect to the weak convergence topology or the stronger Wasserstein metric, under the strong exponential integrability…
We investigate properties of minimal $N$-point Riesz $s$-energy on fractal sets of non-integer dimension, as well as asymptotic behavior of $N$-point configurations that minimize this energy. For $s$ bigger than the dimension of the set…
We compute the full probability distribution of the moment of inertia $I \propto \sum_{i=1}^N \vec{r}_i^{\,2}$ of a gas of $N$ noninteracting bosons trapped in a harmonic potential $V(r) = (1/2)\, m\, \omega^2 r^2$, in all dimensions and at…
We study the local statistical behavior of the super-Coulombic Riesz gas of particles in Euclidean space of arbitrary dimension, with inverse power distance repulsion integrable near $0$, and with a general confinement potential, in a…
We prove the large deviation principle for the conditional Gibbs measure associated with the focusing Gross Pitaevskii equation in the low temperature regime. This conditional measure is of mixed type, being canonical in energy and…