Abstract:
We present some recent progress in the study of two-sided level set percolation of GFF. Thanks to isomorphism, the problem for GFF can be extended to the random walk loop soup (RWLS). We show that the percolation for the occupation field of RWLS at subcritical intensity exhibits a non-trivial phase transition. More importantly, we also obtain some results at criticality intensity, corresponding to the percolation of the two-sided level set of GFF at level $\sqrt{log N}$. As a prerequisite, we derive a useful power-law upper bound for the arm events. This is based on joint works with Pierre Nolin and Wei Qian from City University of Hong Kong.
Biography:
Yifan Gao is currently a Postdoc at City University of Hong Kong. He earned his Ph.D. degree in 2022 from Peking University under the supervision of Professors Fuxi Zhang and Xinyi Li. His research focuses on probability models arising from statistical physics such as Gaussian free field and Brownian loop soup.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
This event is open to the NYU Shanghai community and Math community.