Electronic Communications in Probability

The Center of Mass of the ISE and the Wiener Index of Trees

Svante Janson and Philippe Chassaing

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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.

Article information

Electron. Commun. Probab., Volume 9 (2004), paper no. 20, 178-187.

Accepted: 30 December 2004
First available in Project Euclid: 26 May 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60J85: Applications of branching processes [See also 92Dxx]

ISE Brownian snake Brownian excursion center of mass Wiener index

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Janson, Svante; Chassaing, Philippe. The Center of Mass of the ISE and the Wiener Index of Trees. Electron. Commun. Probab. 9 (2004), paper no. 20, 178--187. doi:10.1214/ECP.v9-1088. https://projecteuclid.org/euclid.ecp/1464286700

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