Scaling of Percolation on Infinite Planar Maps, I

2005/01/01 by Omer Angel, Angel, Omer · 3 citations
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math-ph #math.MP #math.PR #msc:05C80 #msc:60K35 #msc:60K37

paper · pdf · doi:10.48550/arxiv.math/0501006

28 pages, 5 figures

arxiv created 2005/01/01 · arxiv updated 2009/12/01

Abstract

We consider several aspects of the scaling limit of percolation on random planar triangulations, both finite and infinite. The equivalents for random maps of Cardy's formula for the limit under scaling of various crossing probabilities are given. The limit probabilities are expressed in terms of simple events regarding Airy-Levy processes. Some explicit formulas for limit probabilities follow from this relation by applying known results on stable processes. Conversely, natural symmetries of the random maps imply identities concerning the Airy-Levy processes.

Cited by

• Local convergence of large random triangulations coupled with an Ising\n model
• Geometry and percolation on half planar triangulations
• Interfaces in the vertex-decorated Ising model on random triangulations\n of the disk

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