Limit of the Wulff Crystal when approaching criticality for site percolation on the triangular lattice

Duminil-Copin, Hugo

Preprint

English

Limit of the Wulff Crystal when approaching criticality for site percolation on the triangular lattice

Contributors

Duminil-Copin, Hugo

Publication date

2013

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 very modest contribution 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.

Classification

arxiv : math.PR

UNIGE affiliation entities

Faculté des sciences / Section de mathématiques

Citation (ISO format)

DUMINIL-COPIN, Hugo. Limit of the Wulff Crystal when approaching criticality for site percolation on the triangular lattice. 2013.

Preprint

Identifiers

PID : unige:30541
arXiv : 1305.6034

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271downloads

Creation

20/10/2013 22:08:00

First validation

20/10/2013 22:08:00

Update

14/03/2023 20:33:36

Status update

14/03/2023 20:33:36

Last indexation

30/10/2024 14:43:44

Limit of the Wulff Crystal when approaching criticality for site percolation on the triangular lattice

Contributors

Publication date

Abstract

Classification

UNIGE affiliation entities

Citation (ISO format)

Main files (1)

Identifiers

Technical informations

Creation

First validation

Update

Status update

Last indexation