Continuum nonsimple loops and 2D critical percolation

F. Camia, C.M. Newman

    Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

    20 Citaten (Scopus)

    Samenvatting

    Substantial progress has been made in recent years on the 2D critical percolation scaling limit and its conformal invariance properties. In particular, chordal SLE 6(the Stochastic Loewner Evolution with parameter =6) was, in the work of Schramm and of Smirnov, identified as the scaling limit of the critical percolation exploration process. In this paper we use that and other results to construct what we argue is the fullscaling limit of the collection of allclosed contours surrounding the critical percolation clusters on the 2D triangular lattice. This random process or gas of continuum nonsimple loops in Bbb R2is constructed inductively by repeated use of chordal SLE 6. These loops do not cross but do touch each other—indeed, any two loops are connected by a finite path of touching loops.
    Originele taal-2Engels
    Pagina's (van-tot)157-173
    TijdschriftJournal of Statistical Physics
    Volume116
    Nummer van het tijdschrift1-4
    DOI's
    StatusGepubliceerd - 2004

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