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Percolations on random maps I: half-plane models · Around

2013

Percolations on random maps I: half-plane models

Angel, Omer, Curien, Nicolas

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We study Bernoulli percolations on random lattices of the half-plane obtained as local limit of uniform planar triangulations or quadrangulations.

Using the characteristic spatial Markov property or peeling process of these random lattices we prove a surprisingly simple universal formula for the critical threshold for bond and face percolations on these graphs.
Our techniques also permit us to compute off-critical and critical exponents related to percolation clusters such as the volume and the perimeter.

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1982
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With a foreword by Gian-Carlo Rota, Wiley-Interscience Series in Discrete Mathematics
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V. G. Knizhnik, A. M. Polyakov, and A. B. Zamolodchikov
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A statistical field theory approach
J. Ambjørn, B. Durhuus, and T. Jonsson · 1997
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