Abstract:
In this talk, we consider the local time for a critical branching random walk (CBRW). We will begin by a brief introduce of CBRW and integrated super-Brownian excursion (ISE), which serves as limit (after rescaling) of a CBRW. In dimension less than 3, it is known that local time of CBRW converges to that of ISE ([Le Gall and Lin 2015]). And for higher dimensions, their local times (at single points) become trivial. We observe that local time at points can be replaced by local time at hypersurfaces after proper rescaling, in a way that the above convergence can be extended to all dimensions. We also extend the convergence of local time to that of first hitting time under the same framework. This is a joint work with Xinxin Chen and Yueyun Hu.
Biography:
Tianyi Bai obtained his Bachelor degree at Peking University in June 2017. Then he obtained his Master's degree at Université Paris 6th in June 2018, under the supervision of Professor Zhan Shi. He obtained Ph.D. degree at Université Paris 13th in June 2021, under the supervision of Professor Yueyun Hu. Now he is holding a postdoctoral position in New York University Shanghai. His research is mainly about branching random walk, intersection of random walks, and Brownian loop soup.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai