YMSC Probability Seminar

Organizers：

吴昊，杨帆，姜建平，顾陈琳

Speaker：

Xi Geng 耿曦

University of Melbourne

Time：

Thur., 15:40-16:40, Dec. 19, 2024

Venue：

C548, Shuangqing Complex Building A

Title：

Long time behaviour of the parabolic Anderson Model in the hyperbolic space

Abstract:

In this talk, we discuss both the moment and almost-sure asymptotics for the parabolic Anderson model in the hyperbolic space with a time-independent, regular, isometry-invariant Gaussian potential. The moment asymptotics turns out to be identical to the Euclidean case. In particular (which is also a surprising point), the fluctuation exponent is determined by an Euclidean variational problem which is insensitive to the underlying geometry. On the other hand, the almost-sure behaviour becomes drastically different from the Euclidean case: the solution exhibits a much faster growth due to exponential volume growth in negative curvature.

This is based on joint work with Weijun Xu (Peking University) as well as an ongoing project with Weijun and my PhD student Sheng Wang.