Probability Seminar——Growth-fragmentation process in a planar Brownian excursion

Abstract: We consider a Brownian excursion from 0 to 1 in the upper half-plane. It (possibly) makes excursions above the horizontal line of height $t > 0$, and for each such excursion, we record the difference between its ending point and its starting point. Hence for each t, we have a collection of real numbers. We show that the process indexed by $t$ is a growth-fragmentation process that we characterize. Joint work with William Da Silva.