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The asymmetric contact process at its second critical value

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Abstract

The asymmetric contact process onZ has two distinct critical values λ1 > λ2 (at least with sufficient asymmetry). One can consider the process on {0,...,N} and analyze the time (which we call σ N ) till complete vacany starting from complete occupation. Its behavior has already been resolved for all regions of λ except for λ=λ2. For this value, Schinazi proved that lim N→α log σ N /logN=2 in probability and conjectured that σ N /N 2 converges in distribution. It is that result that we prove in this paper. We rely heavily on the Brownian motion behavior of the edge particle, which comes from Galves and Presutti and Kuczek.

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Authors and Affiliations

  1. University of California, Los Angeles, 90095-1555, Los Angeles, California

    Ted Sweet

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  1. Ted Sweet
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Sweet, T. The asymmetric contact process at its second critical value. J Stat Phys 86, 749–764 (1997). https://doi.org/10.1007/BF02199118

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  • DOI: https://doi.org/10.1007/BF02199118

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