Crossing probability in Gaussian Free Field

来源：数学科学学院发布时间：2021-04-26 460

报告人: Professor Hao Wu （Tsinghua University）

时间：2021 年 4 月 26 日下午 3:00 开始

地点：浙江大学（玉泉校区）数学科学学院逸夫工商楼 200-9

Abstract: Two-dimensional Gaussian free field (GFF) is a natural 2D time analogue of Brownian motion. It is also known as free bosonic field in physics literatures, and it is the building block in conformal field theory, quantum gravity and statistical physics. In this talk, we focus on estimates of crossing probability in GFF. Such crossing probability is a delicate quantity for GFF. We will introduce discrete GFF (dGFF) and metric graph GFF (mGFF). Both objects converge to continuum GFF as distributions. However, the crossing probabilities in dGFF and in mGFF are distinct. To derive the scaling limits of crossing probabilities in dGFF and in mGFF, we will introduce Schramm Loewner evolution (SLE). It turns out that the crossing probability in dGFF converges to the so-called pure partition functions of multiple SLEs, and that the crossing probability in mGFF converges to the ``fusion”of pure partition functions.

This talk is based on joint works with J. Ding (UPenn), M. Wirth (UPenn), and with M. Liu

(Tsinghua).

吴昊，2005 年进入清华大学数理基科班。2009 年本科毕业后赴法国读博，主要研究随机过程 Schramm Loewner Evolution，2013 年博士毕业。2013-2017 年，先后在美国麻省理工与瑞士日内瓦大学做博士后，主要研究高斯自由场与 Ising 模型。2017 年，被聘为清华大学长聘教授。2019 年，获得清华大学“学术新人奖”。2020 年，获得北京市自然科学基金杰出青年项目。欢迎参加！

联系人：苏中根, Email： suzhonggen@zju.edu.cn Tel：0571-87953676

浙江大学数学科学学院

浙江大学数据科学中心

2021 年 4 月 14 日