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2013 Limit of the Wulff Crystal when approaching criticality for site percolation on the triangular lattic
Hugo Duminil-Copin
Author Affiliations +
Electron. Commun. Probab. 18: 1-9 (2013). DOI: 10.1214/ECP.v18-3163

Abstract

The understanding of site percolation on the triangular lattice progressed greatly in the last decade. Smirnov proved conformal invariance of critical percolation, thus paving the way for the construction of its scaling limit. Recently, the scaling limit of near critical percolation was also constructed by Garban, Pete and Schramm. The aim of this article is to explain how these results imply the convergence, as $p$ tends to $p_c$, of the Wulff crystal to a Euclidean disk. The main ingredient of the proof is the rotational invariance of the scaling limit of near-critical percolation proved by these three mathematicians.

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Hugo Duminil-Copin. "Limit of the Wulff Crystal when approaching criticality for site percolation on the triangular lattic." Electron. Commun. Probab. 18 1 - 9, 2013. https://doi.org/10.1214/ECP.v18-3163

Information

Accepted: 18 December 2013; Published: 2013
First available in Project Euclid: 7 June 2016

zbMATH: 1307.82005
MathSciNet: MR3151749
Digital Object Identifier: 10.1214/ECP.v18-3163

Subjects:
Primary: 82B20

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