Speaker :    Mr. Guan-Yu Chen 

                   (Ph. D. student in National Chiao Tung University)

 Day 1 

 Time     :    August 10 (Tuesday)  10:30-12:00, 13:00-14:30

 Topic    :    I. Classical results on finite state Markov chains 

                   II. Frequently used metrics and their relationships

  Day 2

  Time     :   August 11 (Wednesday)  10:30-12:00, 13:00-14:30

  Topic    :   III. Cut-offs and pre-cutoffs phenomenon for Markov chains 

                    IV. Recent results in lp -cutoff and open problems

Abstract: 

    The series of talks is to introduce the so-called cut-off phenomenon observed by Aldous and Diaconis in 1980s while studying a family of finite state Markov chains. In the first talk, we recall some classical results on finite state Markov chains. In the second talk, we introduce some frequently used metrics that measure the distance between two probability measures and discuss relations among them. In the third talk, we define the cut-off and precut-off phenomenon for finite Markov chains and introduce some useful techniques through concrete examples (couplings and strong stationary times). In the last talk, we define the lp -cutoff and present some recent results and open problems.

Place :

Lecture Room A,

National Center for Theoretical Sciences

4th Floor, The 3rd General Building,

National TsingHua University