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Title of Journal: J Stat Phys

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Abbravation: Journal of Statistical Physics

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Springer US

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DOI

10.1002/jsfa.2740040605

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1572-9613

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Coarsening Dynamics on mathbb Zd with Froz

Authors: M Damron S M Eckner H Kogan C M Newman V Sidoravicius
Publish Date: 2015/04/09
Volume: 160, Issue: 1, Pages: 60-72
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Abstract

We study Markov processes in which pm 1valued random variables sigma xt xin mathbb Zd update by taking the value of a majority of their nearest neighbors or else tossing a fair coin in case of a tie In the presence of a random environment of frozen plus resp minus vertices with density rho + resp rho we study the prevalence of vertices that are eventually fixed plus or fixed minus or flippers changing forever Our main results are that for rho + 0 and rho =0 all sites are fixed plus while for rho + 0 and rho very small compared to rho + the fixed minus and flippers together do not percolate We also obtain some results for deterministic placement of frozen verticesThe authors thank Leo T Rolla for many fruitful discussions They also thank an anonymous referee for carefully reading the paper and suggesting several additional references The research reported in this paper was supported in part by NSF Grants DMS1007524 SE and CMN DMS1419230 MD and OISE0730136 SE HK and CMN VS was supported by ESFRGLIS network and by Brazilian CNPq Grants 308787/20110 and 476756/20120 and FAPERJ Grant E26/102878/2012BBP

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