Abstract:

Liouville Brownian motion was introduced as a canonical diffusion process under Liouville quantum gravity. It is constructed as a time change of 2-dimensional Brownian motion by the continuous additive functional associated with a Liouville measure, through a regularizing approximation procedure of the Gaussian free field. In this talk, we are concerned with the question whether one can construct Liouville Brownian motion directly from the Liouville measure. We will present a discrete approximation scheme that in fact works for any time-changed Brownian motion by a Revuz measure that has full quasi support. Based on joint work with Yang Yu.

About the Speaker:

陈振庆，美国华盛顿大学 (西雅图) 数学系终身教授，分别于2007年和2014年当选为美国数理统计学会会士和美国数学学会会士。主要从事概率论及随机过程的研究，主要研究方向包括马尔可夫过程和狄氏空间理论、位势理论、随机微分方程、扩散过程、稳定过程以及偏微分方程中的概率方法等。现 (曾) 担任国际著名期刊Potential Analysis的主编以及AOP、AAP、SPA、EJP、JTP、PAMS等期刊编委，2019年荣获伊藤奖(lto Prize)。出版专著一部，在JEMS、MAMS、Math.Ann.、Adv. Math..CMP、AOP、PTRF、TAMS、JFA等顶尖期刊发表论文近200篇。