中国科学院数学与系统科学研究院

科研进展与学术交流报告会

（第62期）

报告人：吴昊 教授（清华大学）

题  目：Connection probabilities for Ising model and their relation to Dyson Brownian motion

摘  要：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.

时  间：2024.3.15(星期五), 10:40-13:00

地  点：南楼204会议室/腾讯会议534-8268-8299