A particular bit of universality : scaling limits of some dependent percolation models

F. Camia, C.M. Newman, V. Sidoravicius

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    11 Citations (Scopus)

    Abstract

    We study families of dependent site percolation models on the triangular lattice and hexagonal lattice 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 .
    Original languageEnglish
    Pages (from-to)311-332
    JournalCommunications in Mathematical Physics
    Volume246
    Issue number2
    DOIs
    Publication statusPublished - 2004

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