Coarsening Dynamics on Z<sup>d</sup> with Frozen Vertices

M. Damron, S. M. Eckner, H. Kogan, Charles Newman, V. Sidoravicius

Research output: Contribution to journalArticle

Abstract

We study Markov processes in which ±1-valued random variables σ<inf>x</inf>(t),x∈Z<sup>d</sup>, 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 ρ<sup>+</sup> (resp., ρ<sup>-</sup>), we study the prevalence of vertices that are (eventually) fixed plus or fixed minus or flippers (changing forever). Our main results are that, for <sup>ρ+</sup>>0 and ρ<sup>-</sup>=0, all sites are fixed plus, while for <sup>ρ+</sup>>0 and <sup>ρ-</sup> very small (compared to <sup>ρ+</sup>), the fixed minus and flippers together do not percolate. We also obtain some results for deterministic placement of frozen vertices.

Original languageEnglish (US)
Pages (from-to)60-72
Number of pages13
JournalJournal of Statistical Physics
Volume160
Issue number1
DOIs
StatePublished - Apr 9 2015

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Coarsening
apexes
Random Environment
Tie
Markov Process
Placement
Nearest Neighbor
Markov processes
Random variable
Update
random variables

Keywords

  • Coarsening models
  • Random environment
  • Zero-temperature Glauber dynamics

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Coarsening Dynamics on Z<sup>d</sup> with Frozen Vertices. / Damron, M.; Eckner, S. M.; Kogan, H.; Newman, Charles; Sidoravicius, V.

In: Journal of Statistical Physics, Vol. 160, No. 1, 09.04.2015, p. 60-72.

Research output: Contribution to journalArticle

Damron, M. ; Eckner, S. M. ; Kogan, H. ; Newman, Charles ; Sidoravicius, V. / Coarsening Dynamics on Z<sup>d</sup> with Frozen Vertices. In: Journal of Statistical Physics. 2015 ; Vol. 160, No. 1. pp. 60-72.
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