Financial & Actuarial Series Seminar-Connection probabilities for 2D critical lattice models


2:00 PM - 3:00 PM



  • Time: 02:00 p.m.-03:00 p.m.
  • Date: April 3, 2023
  • Venue: MA318
  • Speaker: Prof. Hao Wu, Tsinghua University
  • Host: Prof. Youzhou Zhou
  • Topic: Two harmonic Jacobi–Davidson methods for computing a partial generalized singular value decomposition of a large matrix pair


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∈(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.


Professor Hao Wu obtained her Bachelor's degree in Mathematics from Tsinghua University in 2009 and her PhD from Université Paris-Sud in France in 2013. From 2013 to 2017, she worked as a postdoctoral researcher at Massachusetts Institute of Technology in the United States and University of Geneva in Switzerland. In 2017, she was appointed as a tenured professor at Tsinghua University. Prof. Hao Wu's main research focus is on classical statistical physics models such as Schramm Loewner Evolution, Gaussian Free Field, and Ising model. Her notable works include a series of studies on the boundary-point connectivity probability of planar statistical physics models.

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