Annealed upper tails for the energy of a polymer

We study the upper tails for the energy of a randomly charged symmetric and transient random walk. We assume that only charges on the same site interact pairwise. We consider annealed estimates, that is when we average over both randomness, in dimension three or more. We obtain a large deviation principle, and an explicit rate function for a large class of charge distributions.Comment: 36 pages, focus on upper tails; the lower tails estimates make another pape

On large intersection and self-intersection local times in dimension five or more

We show a remarkable similarity between strategies to realize a large intersection or self-intersection local times in dimension five or more. This leads to the same rate functional for large deviation principles for the two objects obtained respectively by Chen and Morters, and by the present author. We also present a new estimate for the distribution of high level sets for a random walk, with application to the geometry of the intersection set of two high level sets of the local times of two independent random walks.Comment: 16 page

On the Dirichlet problem for asymmetric zero-range process on increasing domains

We characterize the principal eigenvalue of the generator of the asymmetric zero-range process in dimensions d>2, with Dirichlet boundary on special domains. We obtain a Donsker-Varadhan variational representation for the principal eigenvalue, and show that the corresponding eigenfunction is unique in a natural class of functions. This allows us to obtain asymptotic hitting time estimates.Comment: 33 pages http://www.cmi.univ-mrs.fr/~assela

Large deviations for Brownian motion in a random scenery

We prove large deviations principles in large time, for the Brownian occupation time in random scenery. The random scenery is constant on unit cubes, and consist of i.i.d. bounded variables, independent of the Brownian motion. This model is a time-continuous version of Kesten and Spitzer's random walk in random scenery. We prove large deviations principles in ``quenched'' and ``annealed'' settings.Comment: 29 page

Sublogarithmic fluctuations for internal DLA

We consider internal diffusion limited aggregation in dimension larger than or equal to two. This is a random cluster growth model, where random walks start at the origin of the d-dimensional lattice, one at a time, and stop moving when reaching a site that is not occupied by previous walks. It is known that the asymptotic shape of the cluster is a sphere. When the dimension is two or more, we have shown in a previous paper that the inner (resp., outer) fluctuations of its radius is at most of order $\log(\mathrm{radius})$ [resp., $\log^2(\mathrm{radius})$]. Using the same approach, we improve the upper bound on the inner fluctuation to $\sqrt{\log(\mathrm{radius})}$ when d is larger than or equal to three. The inner fluctuation is then used to obtain a similar upper bound on the outer fluctuation.Comment: Published in at http://dx.doi.org/10.1214/11-AOP735 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Quenched large deviations for diffusions in a random Gaussian shear flow drift

We prove a full large deviations principle in large time, for a diffusion process with random drift V, which is a centered Gaussian shear flow random field. The large deviations principle is established in a ``quenched'' setting, i.e. is valid almost surely in the randomness of V.Comment: 29 page