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

Svante Janson (1) , Philippe Chassaing (2)

1 Department of Mathematics [Uppsala]
2 IECN - Institut Élie Cartan de Nancy

We 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.

Mots clés: ISE; Brownian snake; Brownian excursion; center of mass; Wiener index

Domaines: Probabilités [math.PR]

Svante Janson, Philippe Chassaing. The center of mass of the ISE and the Wiener index of trees. Electronic Communications in Probability, 2004, 9. ⟨hal-00005089⟩