## EVENT DETAILS AND ABSTRACT

**Probability Seminar**
**Title:** On covering monotonic paths with simple random walk

**Speaker:** Eviatar Procaccia

**Speaker Info:** Texas A&M

**Brief Description:**

**Special Note**:

**Abstract:**

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 dâ‰¥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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