The center of mass of the ISE and the Wiener index of trees

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68594We derive the distribution of the center of mass $S$ of the integrated superBrownian excursion (ISE) {from} the asymptotic distribution of the Wiener index for simple trees. Equivalently, this is the distribution of the integral of a Brownian snake. A recursion formula for the moments and asymptotics for moments and tail probabilities are derived.11 pagesProbability60K35 (Primary), 60J85 (Secondary)The center of mass of the ISE and the Wiener index of treestext