Abstract
We consider the one-dimensional supercritical contact process. LetT v be the first time the process reaches a densityq larger than the equilibrium oneρ in the region [1⋯N]. We prove that, starting from equilibrium,T N /E(T N ) converges to an exponential random time of mean one. In this way we extend previous results of Lebowitz and Schonmann.
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Galves, A., Martinelli, F. & Olivieri, E. Large-density fluctuations for the one-dimensional supercritical contact process. J Stat Phys 55, 639–648 (1989). https://doi.org/10.1007/BF01041602
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DOI: https://doi.org/10.1007/BF01041602