Large deviation principles and generalized Sherrington-Kirkpatrick models
Large deviations for a random walk in dynamical random environment
Large deviations for directed percolation on a thin rectangle
Following the recent investigations of Baik and Suidan in [Int. Math. Res. Not. (2005) 325–337] and Bodineau and Martin in [Electron. Commun. Probab. 10 (2005) 105–112 (electronic)], we prove large deviation properties for a last-passage percolation model in ℤ+2 whose paths are close to the axis. The results are mainly obtained when the random weights are Gaussian or have a finite moment-generating function and rely, as in [J. Baik and T.M. Suidan, Int. Math. Res. Not. (2005) 325–337] and [T. Bodineau...
Large deviations for directed percolation on a thin rectangle
Following the recent investigations of Baik and Suidan in [Int. Math. Res. Not. (2005) 325–337] and Bodineau and Martin in [Electron. Commun. Probab. 10 (2005) 105–112 (electronic)], we prove large deviation properties for a last-passage percolation model in ℤ+2 whose paths are close to the axis. The results are mainly obtained when the random weights are Gaussian or have a finite moment-generating function and rely, as in [J. Baik and T.M. Suidan, Int. Math. Res. Not. (2005) 325–337] and [T. Bodineau...
Large deviations for long range interacting particle systems with jumps
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 the range of an integer valued random walk
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- limit of crossing probabilities, discontinuity, and asymptotic behavior of threshold values in Mandelbrot's fractal percolation process.
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 time asymptotics of growth models on space-like paths. I: Push ASEP.
Large time, small coupling behaviour of a quantum particle in a random field
Large-range constant threshold growth model in one dimension.
Largest minimal percolating sets in hypercubes under 2-bootstrap percolation.
Last passage percolation in macroscopically inhomogeneous media.
Law of the Iterated Logarithm for Tranisitive C... Anosov Flows and Semiflows over Maps of the Interval.
Le concept nouveau de fonctionnelle d'opacité d'une statistique. Étude des relations entre la loi des grands nombres, l'entropie informationnelle et l'entropie statistique
Le rôle de l'énergie libre pour des systèmes régis par l'équation de Fökker-Planck
Lectures on Logarithmic Sobolev Inequalities