Structure of the clusters inside the Brownian loop-soup
报告题目(Title)：Structure of the clusters inside the Brownian loop-soup
报告人(Speaker)：钱玮 (Universite Paris-Saclay)
地点(Place)：Zoom 898 977 810 43 (pw: 123456)
时间(Time)：2021年9月27日 (周一) 下午4:00-5:00
邀请人(Inviter)：何辉
报告摘要
Introduced by Lawler and Werner, Brownian loop-soups have rich relations to various objects in two-dimensional random geometry. At subcritical intensities $c\in(0,1]$, the Brownian loop-soup in the unit disk a.s. contains infinitely many clusters. We study the structure of each individual cluster and show that it is composed of two independent parts. Furthermore, at the critical intensity, the loops that touch the boundary of a cluster can be decomposed into a Poisson point process of excursions. Motivated by the question of reconnecting the excursions into loops, we further investigate the existence of multiple points on the boundary of the clusters, by introducing a generalized disconnection exponent. In order to compute these exponents, we introduce the so-called radial hypergeometric SLEs. The generalized disconnection exponents allow us to obtain the exact dimensions of multiple points on the boundaries of the clusters. This talk is based on a series of works, including several joint works with Wendelin Werner and an undergoing work with Yifan Gao and Xinyi Li.
