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Height and diameter of Brownian tree

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posted on 2023-06-09, 16:48 authored by Minmin WangMinmin Wang
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.

History

Publication status

  • Published

File Version

  • Published version

Journal

Electronic Communications in Probability

ISSN

1083-589X

Publisher

Institute of Mathematical Statistics

Issue

88

Volume

20

Page range

1-15

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Probability and Statistics Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2019-02-08

First Open Access (FOA) Date

2019-02-08

First Compliant Deposit (FCD) Date

2019-02-08

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