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

Mathematics – Probability

Scientific paper

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11 pages

Scientific paper

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.

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