Speaker: Professor Wang Jian
Topic: Quenched local limit theorem for random conductance models with long-range jumps
Date: March 2nd, 2024 (Saturday)
Time: 3.00 p.m.
Venue: Academic Lecture Hall 1506, Jingyuan Building
Sponsors: School of Mathematics and Statistics, Institute of Mathematics, Institute of Science and Technology
Biography:
In 2001, Wang Jian graduated from Mathematics Department of Fujian Normal University and began his work in the university. He achieved the master’s degree from Fujian Normal University in 2004. In September 2005, he got into to Beijing Normal University and studied under Professor Chen Mufa from Beijing Normal University, an academician of Chinese Academy of Sciences. In June 2008, he received a Doctor of Science degree. He was funded by Alexander von Humboldt stifurg in 2009, Japan Society for the Promotion of Science in 2014, National Science Fund for Excellent Young Scholars in 2015, and National Science Fund for Distinguished Young Scholars in 2022.
Abstract:
We establish the quenched local limit theorem for reversible random walk on $\Z^d$ (with $d\ge 2$) among stationary ergodic random conductances that permit jumps of arbitrary length. The proof is based on the weak parabolic Harnack inequalities and on-diagonal heat-kernel estimates for long-range random walks on general ergodic environments. As a byproduct, we prove the maximal inequality with an extra tail term for long-range reversible random walks, which in turn yields the everywhere sublinear property for the associated corrector.