Large deviations for tandem queueing systems.
Large deviations for the empirical measures of reflecting Brownian motion and related constrained processes in .
Large deviations for the largest eigenvalue of rank one deformations of Gaussian ensembles.
Large deviations for the range of an integer valued random walk
Large deviations for transient random walks in random environment on a Galton–Watson tree
Consider a random walk in random environment on a supercritical Galton–Watson tree, and let τn be the hitting time of generation n. The paper presents a large deviation principle for τn/n, both in quenched and annealed cases. Then we investigate the subexponential situation, revealing a polynomial regime similar to the one encountered in one dimension. The paper heavily relies on estimates on the tail distribution of the first regeneration time.
Large deviations for unbounded additive functionals of a Markov process with discrete time (noncompact case).
Large deviations for voter model occupation times in two dimensions
We study the decay rate of large deviation probabilities of occupation times, up to time t, for the voter model η: ℤ2×[0, ∞)→{0, 1} with simple random walk transition kernel, starting from a Bernoulli product distribution with density ρ∈(0, 1). In [Probab. Theory Related Fields77 (1988) 401–413], Bramson, Cox and Griffeath showed that the decay rate order lies in [log(t), log2(t)]. In this paper, we establish the true decay rates depending on the level. We show that the decay rates are log2(t) when...
Large deviations from a macroscopic scaling limit for particle systems with Kac interaction and random potential
Large deviations from the circular law
Large deviations from the circular law
We prove a full large deviations principle, in the scale N2, for the empirical measure of the eigenvalues of an N x N (non self-adjoint) matrix composed of i.i.d. zero mean random variables with variance N-1. The (good) rate function which governs this rate function possesses as unique minimizer the circular law, providing an alternative proof of convergence to the latter. The techniques are related to recent work by Ben Arous and Guionnet, who treat the self-adjoint case. A crucial role...
Large deviations in randomly coloured random graphs.
Large deviations in spaces of stable type
Large deviations of Markov chains indexed by random trees
Large deviations of sums of independent random variables
Large deviations of the first passage time for a random walk with semiexponentially distributed jumps.
Large deviations of U-empirical measures in strong topologies and applications
Large deviations principle by viscosity solutions: the case of diffusions with oblique Lipschitz reflections
We establish a Large Deviations Principle for diffusions with Lipschitz continuous oblique reflections on regular domains. The rate functional is given as the value function of a control problem and is proved to be good. The proof is based on a viscosity solution approach. The idea consists in interpreting the probabilities as the solutions to some PDEs, make the logarithmic transform, pass to the limit, and then identify the action functional as the solution of the limiting equation.
Large deviations upper bounds and central limit theorems for non-commutative functionals of gaussian large random matrices
Large population limit and time behaviour of a stochastic particle model describing an age-structured population
We study a continuous-time discrete population structured by a vector of ages. Individuals reproduce asexually, age and die. The death rate takes interactions into account. Adapting the approach of Fournier and Méléard, we show that in a large population limit, the microscopic process converges to the measure-valued solution of an equation that generalizes the McKendrick-Von Foerster and Gurtin-McCamy PDEs in demography. The large deviations associated with this convergence are studied. The upper-bound...
Large systems of path-repellent Brownian motions in a trap at positive temperature.