Probability Seminar

Title: On covering monotonic paths with simple random walk
Speaker: Eviatar Procaccia
Speaker Info: Texas A&M
Brief Description:
Special Note:

We study 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≥4 and a $\log$ correction for $d=3$. Interesting conjectures and open questions will be presented.
Date: Thursday, September 28, 2017
Time: 3:00PM
Where: Lunt 107
Contact Person: Julian Gold
Contact email:
Contact Phone:
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