The Brownian loop-catcher
Holder： Gefei Cai(Peking University)
Time：2026-09-14 14:00-15:00
Location：WANG Xuan Lecture Theater，Zhi Hua Building-101
Abstract:
We introduce a family of random connected closed subsets of planar Brownian motion, called Brownian loop-catchers, which interpolate between the continuum loop-erased random-walk (LERW) and the Brownian trace. This provides the canonical continuation of Brownian loop soup clusters to central charges $-2\le c<0$. For each such $c$, the corresponding loop-catcher satisfies the following recovery property: adding all loops from an independent Brownian loop soup of intensity $-c/2$ that intersect it recovers the Brownian trace. Furthermore, no such law exists for $c<-2$. We also show that its outer boundary is locally SLE$_\kappa$ with $\kappa = \frac{1}{3}\left(13 - c - \sqrt{(1-c)(25-c)}\right)\in[2,\frac83)$, and the probability that it intersects an interior ball of radius $\varepsilon$ is asymptotically proportional to $|\log\varepsilon|^{-1+\frac{c}{2}}$ when $-2
About the Speaker:
蔡格非，北京大学北京国际数学研究中心在读博士生，2022年本科毕业于北京大学数学科学学院。研究方向为概率论与数学物理，导师为李欣意、孙鑫。
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