Abatract

In this talk, we consider random conductance models with stable-like long range jumps, and obtain the quenched invariance principle (QIP) and a quantitative version of stochastic homogenization for the scaled random walks with explicit polynomial rates up to logarithmic corrections.For QIP, we utilize probabilistic potential theory for the corresponding jump processes, and two essential ingredients of our proof are the tightness estimate and the Hölder regularity of caloric functions for non-elliptic stable-like processes on graphs.On the other hand, the proof of quantitative homogenization result is based on energy estimates of the localized corrector and multi-scale Poincarein equalities for non-local Dirichlet forms.

Speaker

陈昕，上海交通大学数学科学学院教授，国家优秀青年基金获得者。主要从事与随机分析及相关问题的研究，包括泛函不等式，跳过程的随机分析，流形上的随机分析等等。

王健，福建师范大学数学与统计学院教授、博士生导师、国家杰出青年基金获得者。主要从事随机过程与随机分析方向的研究，特别是Lévy型过程的随机分析。