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