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

J. van den Berg, J. Bjornberg, M. Heydenreich

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

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 Kéfi 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 Kéfi et al. (2007).
Original languageEnglish
Pages (from-to)513-537
JournalStochastic Processes and Their Applications
Volume125
Early online date1 Nov 2014
DOIs
Publication statusPublished - 2015

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