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2018 The incipient infinite cluster of the uniform infinite half-planar triangulation
Loïc Richier
Electron. J. Probab. 23: 1-38 (2018). DOI: 10.1214/18-EJP218

Abstract

We introduce the Incipient Infinite Cluster ($\mathsf{IIC} $) in the critical Bernoulli site percolation model on the Uniform Infinite Half-Planar Triangulation ($\mathsf{UIHPT} $), which is the local limit of large random triangulations with a boundary. The $\mathsf{IIC} $ is defined from the $\mathsf{UIHPT} $ by conditioning the open percolation cluster of the origin to be infinite. We prove that the $\mathsf{IIC} $ can be obtained by adding within the $\mathsf{UIHPT} $ an infinite triangulation with a boundary whose distribution is explicit.

Citation

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Loïc Richier. "The incipient infinite cluster of the uniform infinite half-planar triangulation." Electron. J. Probab. 23 1 - 38, 2018. https://doi.org/10.1214/18-EJP218

Information

Received: 29 September 2017; Accepted: 28 August 2018; Published: 2018
First available in Project Euclid: 12 September 2018

zbMATH: 1398.05183
MathSciNet: MR3858917
Digital Object Identifier: 10.1214/18-EJP218

Subjects:
Primary: 05C80, 60K35, 60K37

JOURNAL ARTICLE
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Vol.23 • 2018
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