学术动态

12月10日 | 顾陈琳:Quantitative homogenization of the parabolic and elliptic Green's functions on percolation clusters

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

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。


发布者:张瑛发布时间:2021-12-04浏览次数:10