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


 
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1. Title Title of document Limit of the Wulff Crystal when approaching criticality for site percolation on the triangular lattic
 
2. Creator Author's name, affiliation, country Hugo Duminil-Copin; Université de Genève; Switzerland
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) planar percolation, near-critical regime, surface tension, Wulff crystal
 
3. Subject Subject classification 82B20
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2013-12-18
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/3163
 
10. Identifier Digital Object Identifier 10.1214/ECP.v18-3163
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 18
 
12. Language English=en en
 
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