Connection probabilities for random-cluster model and uniform spanning tree


报告题目: Connection probabilities for random-cluster model and uniform spanning tree

 

报告专家：吴昊教授（清华大学）

报告时间：2022年12月15日下午15:00至16:00

讲座形式：腾讯会议ID：866-168-204，会议密码：8325

报告摘要: Conformal invariance of critical lattice models in two-dimensional has been vigorously studied for decades. The first example where the conformal invariance was rigorously verified was the planar uniform spanning tree (together with loop-erased random walk), proved by Lawler, Schramm and Werner around 2000. Later, the conformal invariance was also verified for Bernoulli percolation (Smirnov 2001), level lines of Gaussian free field (Schramm-Sheffield 2009), and Ising model and FK-Ising model (Chelkak-Smirnov et al 2012). In this talk, we focus on connection probabilities of these critical lattice models in polygons with alternating boundary conditions.

This talk has two parts.

• In the first part, we consider critical random-cluster model with cluster weight $q\in (0,4)$ and give conjectural formulas for connection probabilities of multiple interfaces. The conjectural formulas are proved for q=2, i.e. the FK-Ising model.

• In the second part, we consider uniform spanning tree (UST) and give formulas for connection probabilities of multiple Peano curves. UST can be viewed as the limit of random-cluster model as $q$ goes to 0. Its connection probabilities turn out to be related to logarithmic CFT.

This talk is based on joint works with Yu Feng, Mingchang Liu, and Eveliina Peltola.

 

专家简介：吴昊，2009年本科毕业于清华大学数学系，2013年博士毕业于法国巴黎十一大；2013-2017年，先后在美国麻省理工与瑞士日内瓦大学做博士后；2017年，被聘为清华大学长聘教授。吴昊主要研究随机过程Schramm Loewner Evolution、高斯自由场与伊辛模型等经典统计物理模型。主要代表作包含平面统计物理模型边界点连通概率系列工作等。

 

邀请人：常寅山

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