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May 2015 Classification of half-planar maps
Omer Angel, Gourab Ray
Ann. Probab. 43(3): 1315-1349 (May 2015). DOI: 10.1214/13-AOP891

Abstract

We characterize all translation invariant half-planar maps satisfying a certain natural domain Markov property. For $p$-angulations with $p\ge3$ where all faces are simple, we show that these form a one-parameter family of measures $\mathbb{H}^{(p)}_{\alpha}$. For triangulations, we also establish existence of a phase transition which affects many properties of these maps. The critical maps are the well-known half-plane uniform infinite planar maps. The subcritical maps are identified as all possible limits of uniform measures on finite maps with given boundary and area.

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Omer Angel. Gourab Ray. "Classification of half-planar maps." Ann. Probab. 43 (3) 1315 - 1349, May 2015. https://doi.org/10.1214/13-AOP891

Information

Published: May 2015
First available in Project Euclid: 5 May 2015

zbMATH: 1354.60010
MathSciNet: MR3342664
Digital Object Identifier: 10.1214/13-AOP891

Subjects:
Primary: 51F99 , 60B99

Keywords: domain Markov property , half planar maps , Random maps

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.43 • No. 3 • May 2015
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