时间：2021年12月10日（周五）15：00-16：00
地点：理科大楼A1714会议室
题目：Quantitative homogenization of the parabolic and elliptic Green's functions on percolation clusters
报告人：顾陈琳 上海纽约大学博士后
主持人：俞锦炯 助理教授
主办：统计学院、统计与数据科学前沿理论及应用教育部重点实验室
摘要：
We study the heat kernel and the Green’s function on the infinite supercritical percolation cluster in dimension d ≥ 2 and prove a quantitative homogenization theorem for these functions with an almost optimal rate of convergence. These results are a quantitative version of the local central limit theorem proved by Barlow and Hambly. The proof relies on a structure of renormalization for the infinite percolation cluster introduced by Armstrong and Dario, Gaussian bounds on the heat kernel established by Barlow and tools of the theory of quantitative stochastic homogenization. An important step in the proof is to establish a C0,1-large-scale regularity theory for caloric functions on the infinite cluster and is of independent interest. This is a joint work with Paul Dario.
报告人简介：
顾陈琳，博士，现为上海纽约大学博士后。已于概率学顶级期刊Ann. Probab.，Ann. Appl. Probab.等发表多篇论文。