Reading Seminar on Brownian motion (Spring 2025)
Time: 19:30-21:30 each Saturday generally.
Location：Online Tencent Meeting ID: 533 769 7016.
Organizer： Yuxuan Zong（宗语轩）.
Introduction: Brownian motion is a central object of probability theory, and many of the content and ideas covered in it will be helpful for future research in pure probability. The aim of this seminar is devoted for a conprehensive understanding of Brownian motion and related topics by exploring both macroscopic phenomenon and microscopic properties. We hope this seminar will lay a good foundation for future study and research.
Reference:
[MP] Peter Mörters and Yuval Peres, Brownian Motion, Cambridge University Press.
Schedule:
22, Feb. Yuxuan Zong（宗语轩）, Introduction+Existence, continuity and nondifferentiability of Brownian Motion, [MP] Section 1.1-1.3.
1, Mar. Yuxuan Zong（宗语轩）, Markov property of Brownian Motion, [MP] Section 2.1-2.3.
8, Mar. Jieyang Hu（胡洁洋）, Martingale property, dirichlet Problem, transience and recurrence of Brownian Motion, [MP] Section 2.4, 3.1, 3.2.
15, Mar. Yichen Hu（胡熠辰）, Occupation measure and Green's function of Brownian Motion, [MP] Section 3.3, 3.4.
22, Mar. Fangzhou Luo（罗方舟）, Hausdorff dimension of Brownian Motion, [MP] Chapter 4.
5, Apr. Yuxuan Zong（宗语轩）, Brownian motion and random walk, [MP] Chapter 5.
19, Apr. Zhuoyan Xie（谢卓言）, Brownian local time, [MP] Section 6.1-6.3.
26, Apr. Leda Wang（王乐达）, Stochastic integrals and applications, [MP] Chapter 7.
10, May. Jingbei Song（宋京倍）, Potential theory of Brownian motion, [MP] Chapter 8.
17/24, May. Yijie Bi（毕一介）, Intersections and self-intersections of Brownian paths, [MP] Chapter 9.
？？, Exceptional sets for Brownian motion, [MP] Chapter 10.