On Covering Monotonic Paths with Simple Random Walk
Student No.:50
Time:16:30~17:30, August 18, 2017
Instructor:Yuan Zhang  [University of California, San Diego]
Place:Lecture hall, 3rd floor of Jin Chun Yuan West Building
Starting Date:2017-8-18
Ending Date:2017-8-18

Abstract: In this talk we discuss the probability that a d dimensional simple random walk (or the first L steps of it) covers each point in a nearest neighbor path connecting 0 and the boundary of an L_1 ball. We show that among all such paths, the one that maximizes the covering probability is the monotonic increasing one that stays within distance 1 from the diagonal. As a result, we can obtain an exponential upper bound on the decaying rate of covering probability of any such path when d\ge 4.