# Probability Seminar - Xiaochuan Yang

**Institution:** Michigan State University

**Title:** An invitation to large scale sojourn properties of Brownian motion

**Date: **Thursday, January 25, 2018

**Location: **C405 Wells Hall

**Time: **3:00 PM - 3:50 PM

**Abstract:**

For a one dimensional Brownian motion, we consider the sets of times where Brownian motion stays inside some moving boundaries. The boundaries considered are power functions with the power in [0, 1/2]. Since the usual scaling for Brownian motion at time t is square root of t, the sojourn sets we considered describe the recurrence of a Brownian motion around zero. We give large scale geometric properties of these sets using macroscopic dimensions introduced by Barlow and Taylor in the late 80's. The audience of 881/882 might find this talk interesting.