Height and diameter of Brownian tree

Wang, Minmin (2016) Height and diameter of Brownian tree. Electronic Communications in Probability, 20 (88). pp. 1-15. ISSN 1083-589X

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By computations on generating functions, Szekeres proved in 1983 that the law of the diameter of a uniformly distributed rooted labelled tree with n vertices, rescaled by a factor n^{−1/2}, converges to a distribution whose density is explicit. Aldous observed in 1991 that this limiting distribution is the law of the diameter of the Brownian tree. In our article, we provide a computation of this law which is directly based on the normalized Brownian excursion. Moreover, we provide an explicit formula for the joint law of the height and diameter of the Brownian tree, which is a new result.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Probability and Statistics Research Group
Related URLs:
Depositing User: Minmin Wang
Date Deposited: 08 Feb 2019 14:58
Last Modified: 08 Feb 2019 14:58
URI: http://srodev.sussex.ac.uk/id/eprint/81832

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