Program
One dimensional random walk in random environment
Student No.:50
Time:Tue/Thu 13:00-14:50, 2016-07-07 ~ 2016-08-16(No classes on Aug 9 and 11)
Instructor:Xinxin Chen  [University Lyon 1]
Place:Conference Room 3, Floor 2, Jin Chun Yuan West Building
Starting Date:2016-7-7
Ending Date:2016-8-16

 

 

Description:

 

 

We consider a random walk on Z in a random environment given by i.i.d. random variables. A phase transition on recurrence/transience will be brought out. The velocity problem in the transient case will be considered later. In the recurrent case, the classical result proved by Sinai will also be introduced. If it is possible, we may work on the maximal local time in the recurrent case.

 
 

 

Prerequisite:

 

 

Markov chain, martingale, Brownian motion

 
 

 

Reference:

 

 

Ya. G. Sinai. The limiting behavior of a one-dimensional random walk in a random medium. Theory Probab. Appl., 27:256-268, 1982

 

F. Solomon. Random walks in a random environment. Ann. Probab., 3:1–31, 1975

 

H. Kesten, M. V. Kozlov, F. Spitzer. A limit law for random walk in a random environment. Compositio Math., 30:145-168,1992