The next meeting of the

National Seminar on Probability and Statistics

will be held on December 6, 2023, at 2:00 p.m. in Room 503 of the Institute of Mathematics and Informatics.

A talk on:

Brownian Motion Conditioned to Spend Limited Time Outside a Bounded Interval – An Extreme Example of Entropic Repulsion

will be delivered by

Dominic Т. Schickentanz (TU Darmstadt).

Abstract. We condition a Brownian motion on \(\mathbb{R}_{\ge 0}\) on spending a total of at most \(s>0\) time units outside a bounded interval. We describe the resulting process in terms of an SDE and discuss the surprising result in the context of entropic repulsion. Moreover, we explicitly determine the exact asymptotic behavior of the probability that a Brownian motion on \([0,T]\) spends limited time outside a bounded interval, as \(T\to \infty\).