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Sharpness versus robustness of the percolation transition in 2d contact processes
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
2015 (English)In: Stochastic Processes and their Applications, ISSN 0304-4149, E-ISSN 1879-209X, Vol. 125, no 2, 513-537 p.Article in journal (Refereed) Published
Abstract [en]

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). 

Place, publisher, year, edition, pages
2015. Vol. 125, no 2, 513-537 p.
Keyword [en]
Contact process, Percolation, Sharp thresholds, Approximate zero-one law
National Category
Probability Theory and Statistics
URN: urn:nbn:se:uu:diva-247413DOI: 10.1016/j.spa.2014.09.010ISI: 000349501200005OAI: oai:DiVA.org:uu-247413DiVA: diva2:796757
Available from: 2015-03-20 Created: 2015-03-18 Last updated: 2016-02-17Bibliographically approved

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