Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	吴昊教授,清华大学
Inviter:	中国科学院数学院学术报告会组委
Title:	Connection probabilities for Ising model and their relation to Dyson Brownian motion
Language:	Chinese
Time & Venue:	2024.03.15 10:40-11:50 南楼204教室腾讯会议:534-8268-8299
Abstract:	The Ising model is one of the most studied lattice models in statistical physics. In this talk, we will first present some recent development for Ising model, focusing on the continuity of the phase transition and conformal invariance for the critical phase. In the second part, we focus on 2-dimensional Ising model and give the connection probabilities of multiple Ising interfaces. Such probabilities are related to solutions to BPZ equations in conformal field theory. In the third part, we explain a relation between multiple Ising interfaces and Dyson Brownian motion. Dyson Brownian motion usually describes the movement of trajectory of independent Brownian motions under mutual repulsion. It turns out that, under proper time-parameterization, the driving function of multiple Ising interfaces becomes Dyson Brownian motion. Using such connection, we may translate estimates on Dyson Brownian motion to estimates on multiple Ising interfaces.