No Double Points on the Boundaries of Brownian Loop-soup Clusters at the Critical Intensity

No Double Points on the Boundaries of Brownian Loop-soup Clusters at the Critical Intensity
Topic
No Double Points on the Boundaries of Brownian Loop-soup Clusters at the Critical Intensity
Date & Time
Thursday, October 16, 2025 - 17:00 - 18:00
Speaker
Wei Qian, University of Hong Kong
Location
W923, West Hall, NYU Shanghai New Bund Campus

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Abstract:

We show that there do not exist double points on the boundaries of Brownian loop-soup clusters at the critical intensity. Such double points are closely related to a question of rewiring excursions into loops in the critical Brownian loop soup. In previous works, we have established that the double points on the boundaries of critical Brownian loop-soup clusters have Hausdorff dimension exactly zero.

In a recent work, we develop a unified approach to establish the non-existence of several types of random fractals in the Brownian motion which have dimension zero: Apart from the aforementioned double points on the boundaries of loop-soup clusters, we also show the non-existence of pioneer triple points in the planar Brownian motion, the pioneer double cut points of the planar and three-dimensional Brownian motions.
 
This talk is based on several works, including a recent joint work with Y. Gao, X. Li and R. Liu.
 

Biography:

Wei Qian is an Associate Professor in the Department of Mathematics of the University of Hong Kong. She is currently on leave from the position of Chargée de Recherche in CNRS in France.  She obtained her PhD at ETH Zürich in 2017, under the supervision of Wendelin Werner. Subsequently, she was a Junior Research Fellow at Churchill college in the University of Cambridge, a Chargée de Recherche of CNRS in Université Paris-Saclay, and an Assistant Professor in the City University of Hong Kong.

Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai

This event is open to the NYU Shanghai community and Math community.