The geometry of a critical percolation cluster on the UIPT

2017/01/06 by Gorny, Matthias, Maurel-Segala, Édouard, Singh, Arvind
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1701.01667

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 differs by a factor 2 from those computed previously by Angel and Curien (2015) in the case of critical site percolation on the uniform infinite half-plane triangulation.

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