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Hydrodynamic limit for the d-facilitated exclusion process

发布时间:2022-04-13 浏览量:66

时   间:  2022-04-13 15:00 — 16:00

地   点:  腾讯会议APP2()
报告人:  苏中根
单   位:  浙江大学
邀请人:  张登
备   注:  腾讯会议:582-193-159, 会议密码:123456. 报告人简介:苏中根,浙江大学教授, 博士生导师。 1995 年获复旦大学博士学位,主要从事概率极限理论及其应用研究,内容包括概率集中不等式,随机渗流模型,高维随机矩阵和随机增长过程等。曾多次主持国家自然科学基金面上项目,其科研成果“概率极限理论及其在 Gauss 过程轨道性质方面的应用” (与林正炎、张立新合作) 2003 年获教育部科技进步二等奖;《概率极限理论基础》(与林正炎、陆传荣合著) 2021 年获首届全国优秀教材(高等教育类)二等奖,2002 年荣获全国普通高校优秀教材一等奖。
报告摘要:  

Consider a periodic one-dimensional exclusion process with the dynamical constraint in which the particle at site x is prevented from jumping to x + 1 (or x − 1) unless the sites x − 1, x − 2, . . . , x − d + 1 (or x + 1, x + 2, . . . , x + d − 1) are all occupied and the site x + 1 (or x − 1) is empty. The case d = 2 was introduced by Basu et al. (PR, 2009) and further studied by Blondel et al. ( AIHP, 2020). Provided that the initial profile is suitably smooth and uniformly larger than the critical density (d−1)/d, we prove the macroscopic density profile evolves, under the diffusive time scaling, according to a fast diffusion equation. The main ingredients in this proof are to verify properties of invariant measures like exponential decay of correlations and equivalence of ensembles. The difficulties arising from the constraint number d (d > 2) are overcome by more delicate analysis. This talk is based on a recent work done jointly with Y. Lei (JOTP, 2022).