2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68530We 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.33 pages http://www.cmi.univ-mrs.fr/~asselahProbabilityMathematical Physics60K35(Primary)82C22,60J25(Secondary)text