Related papers: On large deviation regimes for random media models

In various disordered systems or non-equilibrium dynamical models, the large deviations of some observables have been found to display different scalings for rare values bigger or smaller than the typical value. In the present paper, we…

Behind the nice unification provided by the notion of the level 2.5 in the field of large deviations for time-averages over a long Markov trajectory, there are nevertheless very important qualitative differences between the meaning of the…

We consider the standard model of i.i.d. first passage percolation on Z^d given a distribution G on [0, +$\infty$] (including +$\infty$). We suppose that G({0}) > 1 -- p\_c(d), i.e., the edges of positive passage time are in the subcritical…

This article gives an overview of the emerging literature on large deviations for random graphs. Written for the general mathematical audience, the article begins with a short introduction to the theory of large deviations. This is followed…

We study connectivity properties in a probabilistic model for a large mobile ad-hoc network. We consider a large number of participants of the system moving randomly, independently and identically distributed in a large domain, with a…

In long-range percolation on $\mathbb{Z}^d$, points $x$ and $y$ are connected by an edge with probability $1-\exp(-\beta\|x-y\|^{-d-\alpha})$, where $\alpha>0$ is fixed and $\beta \geq 0$ is a parameter. As $d$ and $\alpha$ vary, the model…

We establish central and non-central limit theorems for sequences of functionals of the Gaussian output of an infinitely-wide random neural network on the d-dimensional sphere . We show that the asymptotic behaviour of these functionals as…

We consider directed first passage percolation on the integer lattice, with time constant $\mu$ and passage time $a_{0n}$ from the origin to $(n,0,...,0)$. It is shown that under certain conditions on the passage time distribution, $Ea_{0n}…

Employing the optimal fluctuation method (OFM), we study the large deviation function of long-time averages $(1/T)\int_{-T/2}^{T/2} x^n(t) dt$, $n=1,2, \dots$, of centered stationary Gaussian processes. These processes are correlated and,…

We study a large deviation functional of density fluctuation by analyzing stochastic non-linear diffusion equations driven by the difference between the densities fixed at the boundaries. By using a fundamental equality that yields the…

We investigate the statistics of the gap, G_n, between the two rightmost positions of a Markovian one-dimensional random walker (RW) after n time steps and of the duration, L_n, which separates the occurrence of these two extremal…

The aim of the paper is to establish a large deviation principle (LDP) for the empirical measure of mean-field interacting diffusions in a random environment. The point is to derive such a result once the environment has been frozen…

We study large deviations, over a long time window $T \to \infty$, of the dynamical observables $A_n = \int_{0}^{T} x^n(t) dt$, $n=3,4,\dots$, where $x(t)$ is a centered stationary Gaussian process in continuous time. We show that, for…

Let $T$ be a random ergodic pseudometric over $\mathbb R^d$. This setting generalizes the classical \emph{first passage percolation} (FPP) over $\mathbb Z^d$. We provide simple conditions on $T$, the decay of instant one-arms and…

We investigate properties of two-dimensional finite-scale percolation systems whose size along the current flow is smaller than the perpendicular size. Successive thresholds of appearing multiple percolation channels in such systems have…

The location and nature of the percolation transition in random networks is a subject of intense interest. Recently, a series of graph evolution processes have been introduced that lead to discontinuous percolation transitions where the…

Linear diffusions are used to model a large number of stochastic processes in physics, including small mechanical and electrical systems perturbed by thermal noise, as well as Brownian particles controlled by electrical and optical forces.…

This paper studies large deviation principles and weak convergence, both at the level of finite-dimensional distributions and in functional form, for a class of continuous, isotropic, centered Gaussian random fields defined on the unit…

Using martingale methods, we obtain some upper bounds for large and moderate deviations of products of independent and identically distributed elements of GL d (R). We investigate all the possible moment conditions, from super-exponential…

We identify and analyze a surprising phenomenon of Latent Diffusion Models (LDMs) where the final steps of the diffusion can degrade sample quality. In contrast to conventional arguments that justify early stopping for numerical stability,…