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

2003/09/17 by Svante Janson, Janson, Svante, Philippe Chassaing +1
Mathematics · #60J85 (Secondary) #60K35 (Primary) #FOS: Mathematics #Graph theory and applications #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #math.PR #msc:60J85 #msc:60K35

paper · pdf · doi:10.48550/arxiv.math/0309284

11 pages

arxiv created 2003/09/17 · openalex publication_date 2003/09/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Note on the density of ISE and a related diffusion
• Some explicit distributions for Brownian motion indexed by the Brownian tree
• Precise logarithmic asymptotics for the right tails of some limit random variables for random trees
• Conditioned Brownian trees
• Asymptotic Distribution of Brownian Excursions into an Interval