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November 2018 The geometry of a critical percolation cluster on the UIPT
Matthias Gorny, Édouard Maurel-Segala, Arvind Singh
Ann. Inst. H. Poincaré Probab. Statist. 54(4): 2203-2238 (November 2018). DOI: 10.1214/17-AIHP869

Abstract

We consider a critical Bernoulli site percolation on the uniform infinite planar triangulation. We study the tail distributions of the peeling time, perimeter, and volume of the hull of a critical cluster. The exponents obtained here differ by a factor $2$ from those computed previously by Angel and Curien [Ann. Inst. Henri Poincaré Probab. Stat. 51 (2015) 405–431] in the case of critical site percolation on the uniform infinite half-plane triangulation.

Nous examinons le modèle de percolation de Bernoulli par sites critique sur la triangulation infinie uniforme du plan. Nous étudions les queues de distribution du temps d’exploration, du périmètre et du volume de l’enveloppe d’une composante connexe. Les exposants obtenus diffèrent d’un facteur $2$ de ceux calculés auparavant par Angel et Curien [Ann. Inst. Henri Poincaré Probab. Stat. 51 (2015) 405–431] dans le cas de la percolation critique par site sur la triangulation uniforme du demi-plan.

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Matthias Gorny. Édouard Maurel-Segala. Arvind Singh. "The geometry of a critical percolation cluster on the UIPT." Ann. Inst. H. Poincaré Probab. Statist. 54 (4) 2203 - 2238, November 2018. https://doi.org/10.1214/17-AIHP869

Information

Received: 10 January 2017; Revised: 16 October 2017; Accepted: 16 October 2017; Published: November 2018
First available in Project Euclid: 18 October 2018

zbMATH: 06996563
MathSciNet: MR3865671
Digital Object Identifier: 10.1214/17-AIHP869

Subjects:
Primary: 05C80 , 60K35

Keywords: Critical exponents , percolation , Random planar triangulation

Rights: Copyright © 2018 Institut Henri Poincaré

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Vol.54 • No. 4 • November 2018
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