Seminars and Talks
 Current Location：homepage  Seminars and Talks
 Connection probabilities for 2D critical lattice model
 发布人：许全华  发布时间：2023-03-14   浏览次数:53
 Title：Connection probabilities for 2D critical lattice modelSpeaker: Hao Wu（Tsinghua University）Time: Friday, March 17, 2023, 15:30-16:30 Location:Tencent Meeting, Meeting ID:893 4129 1815Abstract: 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 Ising model and give the crossing probabilities of multiple interfaces. Such probabilities are related to solutions to BPZ equations in conformal field theory.• In the second 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.Sponsors：Harbin Institute of Technology, Wuhan University