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  • 标题:Limit of the Wulff Crystal when approaching criticality for site percolation on the triangular lattic
  • 本地全文:下载
  • 作者:Duminil-Copin, Hugo
  • 期刊名称:Electronic Communications in Probability
  • 印刷版ISSN:1083-589X
  • 出版年度:2013
  • 卷号:18
  • 页码:1-9
  • DOI:10.1214/ECP.v18-3163
  • 语种:English
  • 出版社:Electronic Communications in Probability
  • 摘要: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.
  • 关键词:planar percolation, near-critical regime, surface tension, Wulff crystal;82B20
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