Related papers: Large deviations for hyperbolic $k$-nearest neighb…
Large deviation principles are established for the two-parameter Poisson-Dirichlet distribution and two-parameter Dirichlet process when parameter $\theta$ approaches infinity. The motivation for these results is to understand the…
Let $(k_n)_{n \in \mathbb{N}}$ be a sequence of positive integers growing to infinity at a sublinear rate, $k_n \rightarrow \infty$ and $k_n/n \rightarrow 0$ as $n \rightarrow \infty$. Given a sequence of $n$-dimensional random vectors…
In this paper, we proved moderate deviation principles for a fully coupled two-time-scale stochastic systems, where the slow process is given by stochastic differential equations with small noise, while the fast process is a rapidly…
We establish sample-path large deviation principles for the centered cumulative functional of marked Poisson cluster processes in the Skorokhod space equipped with the M1 topology, under joint regular variation assumptions on the marks and…
We consider the stationary measure of the asymmetric simple exclusion process (ASEP) on a finite interval in $\mathbb{Z}$ with open boundaries. Fixing all the jump rates and letting the system size approach infinity, the height profile of…
We study trajectories of d-dimensional Brownian Motion in Poissonian potential up to the hitting time of a distant hyper-plane. Our Poissonian potential V can be associated to a field of traps whose centers location is given by a Poisson…
We prove a large deviations principle for the empirical measure of the one dimensional symmetric simple exclusion process in contact with reservoirs. The dynamics of the reservoirs is slowed down with respect to the dynamics of the system,…
We derive a central limit theorem for the number of vertices of convex polytopes induced by stationary Poisson hyperplane processes in $\mathbb{R}^d$. This result generalizes an earlier one proved by Paroux [Adv. in Appl. Probab. 30 (1998)…
Large deviation for Markov processes can be studied by Hamilton--Jacobi equation techniques. The method of proof involves three steps: First, we apply a nonlinear transform to generators of the Markov processes, and verify that limit of the…
This paper studies large deviations of a ``fully coupled" finite state mean-field interacting particle system in a fast varying environment. The empirical measure of the particles evolves in the slow time scale and the random environment…
Suppose that $Z$ is a random closed subset of the hyperbolic plane $\H^2$, whose law is invariant under isometries of $\H^2$. We prove that if the probability that $Z$ contains a fixed ball of radius 1 is larger than some universal constant…
Consider a family of Boolean models, indexed by integers $n \ge 1$, where the $n$-th model features a Poisson point process in ${\mathbb{R}}^n$ of intensity $e^{n \rho_n}$ with $\rho_n \to \rho$ as $n \to \infty$, and balls of independent…
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…
The purpose of this paper is to ensure the conditions of G\"artner-Ellis Theorem for evaluations of the empirical measure. We show that up-to-date conditions for ensuring the convergence to a quasi-stationary distribution can be applied…
We study large deviations for some non-local parabolic type equations. We show that, under some assumptions on the non-local term, problems defined in a bounded domain converge with an exponential rate to the solution of the problem defined…
Branching Brownian Motion describes a system of particles which diffuse in space and split into offsprings according to a certain random mechanism. In virtue of the groundbreaking work by M. Bramson on the convergence of solutions of the…
We introduce a continuum percolation model defined on the points of a d-dimensional homogeneous Poisson process. Each Poisson point is connected to all points within its connection range, which depends on the distances to the other Poisson…
The large deviations analysis of solutions to stochastic differential equations and related processes is often based on approximation. The construction and justification of the approximations can be onerous, especially in the case where the…
Shot noise processes are used in applied probability to model a variety of physical systems in, for example, teletraffic theory, insurance and risk theory and in the engineering sciences. In this work we prove a large deviation principle…
We consider the path approximation of Bessel processes and develop a new and efficient algorithm. This study is based on a recent work by the authors, on the path approximation of the Brownian motion, and on the construction of specific own…