自由边界条件下Ising模型交叉概率的保形不变性

IF 1.2 2区数学 Q2 STATISTICS & PROBABILITY Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2014-10-14 DOI:10.1214/15-AIHP698

S. Benoist, H. Duminil-Copin, C. Hongler

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引用次数: 28

摘要

我们证明了具有自由边界条件的临界平面Ising模型的交叉概率在尺度极限下是保形不变的，这是由Langlands, Lewis和Saint-Aubin (J. Stat. Phys. 98(2000) 131-244)首次用数值方法研究的现象。我们通过建立针对SLE(3， -3/2， -3/2)的某些探索过程的收敛性来做到这一点。我们还构造了一个自由边界条件的探索树，类似于谢菲尔德(杜克数学)引入的树。J. 147(2009) 79-129。

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Conformal invariance of crossing probabilities for the Ising model with free boundary conditions

We prove that crossing probabilities for the critical planar Ising model with free boundary conditions are conformally invariant in the scaling limit, a phenomenon first investigated numerically by Langlands, Lewis and Saint-Aubin (J. Stat. Phys. 98 (2000) 131-244). We do so by establishing the convergence of certain exploration processes towards SLE(3, -3/2, -3/2). We also construct an exploration tree for free boundary conditions, analogous to the one introduced by Sheffield (Duke Math. J. 147 (2009) 79-129).

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来源期刊

Annales De L Institut Henri Poincare-probabilites Et Statistiques 数学-统计学与概率论

CiteScore

2.70

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Probability and Statistics section of the Annales de l’Institut Henri Poincaré is an international journal which publishes high quality research papers. The journal deals with all aspects of modern probability theory and mathematical statistics, as well as with their applications.