Large deviations for mixtures.
Large deviations for multiple Wiener-Itô integral processes
Large deviations for one dimensional diffusions with a strong drift.
Large deviations for partition functions of directed polymers in an IID field
Consider the partition function of a directed polymer in ℤd, d≥1, in an IID field. We assume that both tails of the negative and the positive part of the field are at least as light as exponential. It is well known that the free energy of the polymer is equal to a deterministic constant for almost every realization of the field and that the upper tail of the large deviations is exponential. The lower tail of the large deviations is typically lighter than exponential. In this paper we obtain sharp...
Large deviations for quasi-arithmetically self-normalized random variables
We introduce a family of convex (concave) functions called sup (inf) of powers, which are used as generator functions for a special type of quasi-arithmetic means. Using these means, we generalize the large deviation result on self-normalized statistics that was obtained in the homogeneous case by [Q.-M. Shao, Self-normalized large deviations. Ann. Probab. 25 (1997) 285–328]. Furthermore, in the homogenous case, we derive the Bahadur exact slope for tests using self-normalized statistics.
Large deviations for random walks with nonidentically distributed jumps having infinite variance.
Large deviations for Riesz potentials of additive processes
We study functionals of the form ζt=∫0t⋯∫0t|X1(s1)+⋯+Xp(sp)|−σ ds1 ⋯ dsp, where X1(t), …, Xp(t) are i.i.d. d-dimensional symmetric stable processes of index 0<β≤2. We obtain results about the large deviations and laws of the iterated logarithm for ζt.
Large deviations for rough paths of the fractional brownian motion
Large deviations for sample paths of Gaussian processes quadratic variations.
Large deviations for some Poisson random integrals
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...