平面临界渗流的保形不变尺度极限

IF 1.3 Q2 STATISTICS & PROBABILITY Probability Surveys Pub Date : 2009-11-02 DOI:10.1214//11-PS180
Nike Sun
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引用次数: 28

摘要

这是在平面临界渗流的尺度极限中出现的保形不变性的介绍性说明。给出了关于三角格上点渗中交叉概率共形不变性的Smirnov定理(2001)。我们还介绍了Schramm- loewner进化(SLE),这是Schramm(2000)发现的一组共形不变随机曲线的单参数族。本文组织的目的是为了证明Smirnov(2001)和Camia和Newman(2007)的结果,即渗透勘探路径在尺度极限上收敛于弦索SLE 6。除了一些一般的复杂分析和概率论之外,不假设任何先验知识。
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Conformally invariant scaling limits in planar critical percolation
This is an introductory account of the emergence of conformal invariance in the scaling limit of planar critical percolation. We give an exposition of Smirnov's theorem (2001) on the conformal invariance of crossing probabilities in site percolation on the triangular lattice. We also give an introductory account of Schramm-Loewner evolutions (SLE ĸ ), a one-parameter family of conformally invariant random curves discovered by Schramm (2000). The article is organized around the aim of proving the result, due to Smirnov (2001) and to Camia and Newman (2007), that the percolation exploration path converges in the scaling limit to chordal SLE 6 . No prior knowledge is assumed beyond some general complex analysis and probability theory.
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来源期刊
Probability Surveys
Probability Surveys STATISTICS & PROBABILITY-
CiteScore
4.70
自引率
0.00%
发文量
9
期刊最新文献
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