时间：2026年7月3日（星期五）10:00-12:15
地点：西湖大学云谷校区E14-301
主讲人：耿曦 墨尔本大学
报告题目：Long Time Asymptotics of Parabolic Anderson Model in the Hyperbolic Space
报告摘要：In this talk, we investigate the quenched long time asymptotic behaviour of the parabolic Anderson model in the hyperbolic space with a time-independent, regular Gaussian potential. The growth of the solution is different from the Euclidean situation; the logarithmic growth rate is t^(5/3) in contrast to t\sqrt{log t} as in the Euclidean case and the exact growth constant is determined through an explicit optimisation procedure. The hyperbolic situation also reveals a stronger non-Euclidean localisation mechanism. We will examine this hidden mechanism governing the growth asymptotics from two different perspectives: Brownian motion localisation and eigenfunction concentration. We will also discuss some further questions and ongoing progress towards the singular white noise case.
This is based on joint work with Weijun Xu (Westlake University) and Sheng Wang (SISSA) as well as ongoing work with Weijun, Adair da Silva Neto (University of Melbourne) and Haiyi Wang (Peking University).
主讲人：周百舸 清华大学
报告题目：Quadratic fluctuations of speed-change Kawasaki dynamics
报告摘要：For the speed-change Kawasaki dynamics under equilibrium measure, we study the weak convergence of its quadratic field, and derive the scaling limit as a nonlinear fluctuation process. This extends the result of Goncalves and Jara [ALEA, Lat. Am. J. Probab. Math. Stat. 16, 605–632 (2019)] to the non-gradient case. This is a joint work with Prof. Chenlin Gu (Tsinghua).
