Graduate Probability Seminar

We meet every Thursday 2 - 2:50 pm, in CIF 3038.

This semester, we are planning to learn about random walks. We will use two references: Random Walk: A Modern Introduction, by G. Lawler and V. Limic (link), and Modern Discrete Probability, by S. Roch (link). We plan to focus on random walks from the first book, while exploring some broader methods and connections from the second, including hitting times, Green’s functions, potential theory, coupling methods, and applications in electrical networks.

If you want to give a talk, please contact one of the organizers.

• September 3: Rui Yu, Liyuan Xu
  Title: Introduction to Random Walks and Organization Meeting
  Abstract: N/A

• September 10: Rui Yu
  Title:  Green’s function of random walks
  Abstract: This talk will be based primarily on Chapter 4 of Lawler and Limic’s Random Walk: A Modern Introduction. We give an overview of Chapter 4, introducing the Green’s function and its main properties. Particular attention will be given to Section 4.6, which studies the Green function for a random walk killed upon leaving a domain and relates expected occupation times to hitting probabilities. Finally, we will discuss some applications of Green function asymptotics, including the dimension-dependent behavior of intersections between independent random walks.

• September 17: TBA
  Title: TBA
  Abstract: TBA

• September 24: TBA
  Title: TBA
  Abstract: TBA

• October 1:
  Title: TBA
  Abstract: TBA

• October 8: TBA
  Title: TBA
  Abstract: TBA

• October 15: Cancelled (Midwest Probability Colloquium)
  Title: N/A
  Abstract: N/A

• October 22: TBA
  Title: TBA
  Abstract: TBA

• October 29: TBA
  Title: TBA
  Abstract: TBA

• November 5: TBA
  Title: TBA
  Abstract: TBA

• November 12: TBA
  Title: TBA
  Abstract: TBA

• November 19: TBA
  Title: TBA
  Abstract: TBA

• December 3: TBA
  Title: TBA
  Abstract: TBA