On the Dirichlet problem for asymmetric zero-range process on increasing domains
arXiv:math/0309181
Abstract
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.
33 pages http://www.cmi.univ-mrs.fr/~asselah