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On the Dirichlet problem for asymmetric zero-range process on increasing domains
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  • Published: 05 July 2004

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

  • Amine Asselah1 

Probability Theory and Related Fields volume 131, pages 62–96 (2005)Cite this article

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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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Authors and Affiliations

  1. C.M.I., Université de Provence, 39 Rue Joliot-Curie, F-13453, Marseille cedex 13, France

    Amine Asselah

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  1. Amine Asselah
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Correspondence to Amine Asselah.

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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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  • Received: 12 November 2003

  • Revised: 18 March 2004

  • Published: 05 July 2004

  • Issue Date: January 2005

  • DOI: https://doi.org/10.1007/s00440-004-0367-6

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Key words or phrases:

  • Principal Dirichlet eigenvalue
  • Particle system
  • Donsker-Varadhan formula
  • Hitting times
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