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

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

2003-09-10

arxiv.org/abs/math/0309181v1

Mathematics

Probability

33 pages http://www.cmi.univ-mrs.fr/~asselah

Scientific paper

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.

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