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Mean-Field Criticality for Percolation on Planar Non-Amenable Graphs

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Abstract:

The critical exponents β, γ, δ and Δ are proved to exist and to take their mean-field values for independent percolation on the following classes of infinite, locally finite, connected transitive graphs: (1) Non-amenable planar with one end. (2) Unimodular with infinitely many ends.

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Authors and Affiliations

  1. Department of Mathematics, University of California at Los Angeles, Los Angeles, CA 90095, USA.¶E-mail: rhs@math.ucla.edu, , , , , , US

    Roberto H. Schonmann

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  1. Roberto H. Schonmann
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Received: 4 April 2001 / Accepted: 4 October 2001

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Schonmann, R. Mean-Field Criticality for Percolation on Planar Non-Amenable Graphs. Commun. Math. Phys. 225, 453–463 (2002). https://doi.org/10.1007/s002200100587

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  • DOI: https://doi.org/10.1007/s002200100587

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