报告题目：Intersection exponents and Brownian fractals

报告时间：2025-04-18  08:30-10:00

报 告 人：高一帆  博士后（香港城市大学）

报告地点：雷军科技楼六楼报告厅（601）

Abstract：The Brownian intersection exponents are computed by Lawler, Schramm and Werner (Acta Math, 2001a, 2001b, 2002) [conjectured by Duplantier and Kwon (Phys Rev Lett, 1988)]. These exponents are useful in determining the Hausdorff dimension of some exceptional sets of planar Brownian motion. In this talk, we discuss our recent development on such exponents. First, we show that a family of generalized exponents can be related to the fractal geometry of the Brownian loop soup (a Poissonian ensemble of Brownian loops in 2D). Second, we prove that the corresponding 3D exponents are analytic, which remains open to this day.