The Brownian loop soup, introduced by Lawler and Werner in 2004, plays a crucial role in understanding two-dimensional models in statistical physics. In this talk, I will present the fractal property of the Brownian loop soup by the Hausdorff dimension of multiple points on the boundaries of clusters. The first part of the talk is to review the well-known results on the Hausdorff dimension of special points of the Brownian motion, which is intimately related to a family of exponents. In the second part, I will explain how to obtain our result via generalizing such exponents to the Brownian loop soup. The challenge is to prove a corresponding separation lemma which is unclear due to the interplay of Brownian motions and the Brownian loop soup. I will highlight this powerful lemma with a final remark on its use in our future work. Based on a joint work (arXiv:2205.11468) with Xinyi Li (Peking University) and Wei Qian (City University of Hong Kong).

24 Feb 2023
4:00pm - 5:30pm
Where
Room 1511 (Lift 27-28), Academic Building, HKUST
Speakers/Performers
Dr. Yifan Gao
CityU HK
Organizer(S)
Department of Mathematics
Contact/Enquiries
Payment Details
Audience
Alumni, Faculty and staff, PG students, UG students
Language(s)
English
Other Events
24 Mar 2025
Seminar, Lecture, Talk
IAS / School of Science Joint Lecture - Pushing the Limit of Nonlinear Vibrational Spectroscopy for Molecular Surfaces/Interfaces Studies
Abstract Surfaces and interfaces are ubiquitous in Nature. Sum-frequency generation vibrational spectroscopy (SFG-VS) is a powerful surface/interface selective and sub-monolayer sensitive spect...
22 Nov 2024
Seminar, Lecture, Talk
IAS / School of Science Joint Lecture - Leveraging Protein Dynamics Memory with Machine Learning to Advance Drug Design: From Antibiotics to Targeted Protein Degradation
Abstract Protein dynamics are fundamental to protein function and encode complex biomolecular mechanisms. Although Markov state models have made it possible to capture long-timescale protein co...