报告题目 (Title)：Quenched and annealed heat kernel estimates for Brox's diffusion（Brox 扩散模型在淬火和退火下的热核估计）
报告人 (Speaker)：王健 教授（福建师范大学）
报告时间 (Time)：2025年9月2日 (周二) 16：30-17:30
报告地点 (Place)：校本部 GJ303
邀请人(Inviter)：阳芬芬
主办部门：太阳集团tyc539数学系
报告摘要：Brox's diffusion is a typical one-dimensional singular diffusion, which was introduced by Brox (1986) as a continuous analogue of Sinai's random walk. In this paper, we establish quenched heat kernel estimates for short time and annealed heat kernel estimates for large time of Brox's diffusion. The proofs are based on Brox's construction via the scale-transformation and the time-change as well as the theory of resistance forms for symmetric strongly recurrent Markov processes. We emphasize that, since the reference measure of Brox's diffusion does not satisfy the so-called volume doubling conditions neither for the small scale nor the large scale, heat kernel estimates of Brox's diffusion are different from diffusions on ergodic random media, and new techniques are required to establish both quenched and annealed heat kernel estimates.
