A Particular Bit of Universality: Scaling Limits of Some Dependent Percolation Models

Federico Camia, Charles M. Newman, Vladas Sidoravicius

Research output: Contribution to journalArticle

Abstract

We study families of dependent site percolation models on the triangular lattice double struck T sign and hexagonal lattice ℍ that arise by applying certain cellular automata to independent percolation configurations. We analyze the scaling limit of such models and show that the distance between macroscopic portions of cluster boundaries of any two percolation models within one of our families goes to zero almost surely in the scaling limit. It follows that each of these cellular automaton generated dependent percolation models has the same scaling limit (in the sense of Aizenman-Burchard [3]) as independent site percolation on double struck T sign.

Original languageEnglish (US)
Pages (from-to)311-332
Number of pages22
JournalCommunications In Mathematical Physics
Volume246
Issue number2
DOIs
StatePublished - Apr 2004

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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