Sharpness versus robustness of the percolation transition in 2d contact processes

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:125

Article

van den Berg, J.^1,2  Bjornberg, J. E.³  Heydenreichd, M.^1,4 

[1] Ctr Wiskunde & Informat, NL-1090 GB Amsterdam, Netherlands

[2] Vrije Univ Amsterdam, Amsterdam, Netherlands

[3] Uppsala Univ, Dept Math, S-75106 Uppsala, Sweden

[4] Leiden Univ, Math Inst, NL-2300 RA Leiden, Netherlands

关键词: Contact process;    Percolation;    Sharp thresholds;    Approximate zero-one law;   

DOI  :  10.1016/j.spa.2014.09.010

来源: Elsevier

【 摘 要 】

We study versions of the contact process with three states, and with infections occurring at a rate depending on the overall infection density. Motivated by a model described in Kefi et al. (2007) for vegetation patterns in arid landscapes, we focus on percolation under invariant measures of such processes. We prove that the percolation transition is sharp (for one of our models this requires a reasonable assumption). This is shown to contradict a form of 'robust critical behaviour' with power law cluster size distribution for a range of parameter values, as suggested in Kefi et al. (2007). (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

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