Brownian motion conditioned to spend limited time outside a bounded interval -- an extreme example of entropic repulsion

Frank Aurzada, Martin Kolb, Dominic T. Schickentanz

We show that a Brownian motion on ${\mathbb{R}}_{\ge 0}$ which is allowed to spend a total of $s>0$ time units outside a bounded interval does not leave the interval at all. This c…