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

Amine Asselah
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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.

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Amine Asselah. 2003-09-10. On the Dirichlet problem for asymmetric zero-range process on increasing domains. https://arxiv.org/abs/math/0309181

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