Probability Seminar——Long time behaviour of the parabolic Anderson Model in the hyperbolic space
报告人：耿曦（University of Melbourne）
时间：2024-12-23 15:30-16:30
地点：智华楼-王选报告厅
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.
Bio：
Xi Geng obtained his PhD from University of Oxford in 2015, did postdoc research at Oxford and CMU, before moving to faculty position in Melbourne in 2019. His research interests are primarily in stochastic analysis and rough paths.
