Three-point connectivity in critical planar percolation
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Where
Title:
Three-point connectivity in critical planar percolation
Speaker: Morris Ang, UCSD
Abstract:
Percolation is a simple random model for studying how connectivity arises in disordered systems. For instance, it describes how water permeates a porous material. At its critical point, two-dimensional percolation exhibits deep links with complex analysis and quantum field theory.
I will discuss the probability that three given points in the plane belong to the same connected component at criticality. A conjecture from conformal field theory predicts that, after proper normalization, this probability converges in the scaling limit to a universal quantity known as the imaginary DOZZ formula. Our proof depends on two central objects from random conformal geometry: curves called Schramm–Loewner evolution and surfaces called Liouville quantum gravity.
This is based on joint work with Gefei Cai, Xin Sun, and Baojun Wu.