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2010 Trees, Animals, and Percolation on Hyperbolic Lattices
Neal Madras, C. Wu
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Electron. J. Probab. 15: 2019-2040 (2010). DOI: 10.1214/EJP.v15-837

Abstract

We study lattice trees, lattice animals, and percolation on non-Euclidean lattices that correspond to regular tessellations of two- and three-dimensional hyperbolic space. We prove that critical exponents of these models take on their mean field values. Our methods are mainly combinatorial and geometric.

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Neal Madras. C. Wu. "Trees, Animals, and Percolation on Hyperbolic Lattices." Electron. J. Probab. 15 2019 - 2040, 2010. https://doi.org/10.1214/EJP.v15-837

Information

Accepted: 3 December 2010; Published: 2010
First available in Project Euclid: 1 June 2016

zbMATH: 1226.60133
MathSciNet: MR2745724
Digital Object Identifier: 10.1214/EJP.v15-837

Subjects:
Primary: 60K35
Secondary: 05B45 , 51M09 , 82B41 , 82B43

Keywords: Critical exponents , hyperbolic geometry , hyperbolic lattice , lattice animal , lattice tree , mean field behaviour , percolation

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Vol.15 • 2010
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