Abstract.
In order to obtain hitting time estimates for the asymmetric zero-range process (AZRP) on ℤd, in dimensions d≥3, we characterize the principal eigenvalue of the generator of the AZRP with Dirichlet boundary on special domains. We obtain a Donsker-Varadhan variational representation and show that the corresponding eigenfunction is unique in a natural class of functions.
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Mathematics Subject Classification (2000):60K35, 82C22, 60J25
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Asselah, A. On the Dirichlet problem for asymmetric zero-range process on increasing domains. Probab. Theory Relat. Fields 131, 62–96 (2005). https://doi.org/10.1007/s00440-004-0367-6
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DOI: https://doi.org/10.1007/s00440-004-0367-6