Reversal property of the Brownian tree

Romain Abraham; Jean François Delmas

doi:10.30757/ALEA.V15-48

Reversal property of the Brownian tree

Romain Abraham
, Jean François Delmas

conventionnée avec l'Université d'Orléans

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the Brownian tree introduced by Aldous and the associated Q-process which consists in an infinite spine on which are grafted independent Brownian trees. We present a reversal procedure on these trees that consists in looking at the tree downward from its top: the branching points becoming leaves and leaves becoming branching points. We prove that the distribution of this tree is invariant under this reversal procedure, which provides a better understanding of previous results from Bi and Delmas (2016).

Original language	English
Pages (from-to)	293-1309
Number of pages	1017
Journal	Alea (Rio de Janeiro)
Volume	15
Issue number	2
DOIs	https://doi.org/10.30757/ALEA.V15-48
Publication status	Published - 1 Jan 2018

Keywords

Genealogical trees
Real trees
Stationary branching processes

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10.30757/ALEA.V15-48

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title = "Reversal property of the Brownian tree",

abstract = "We consider the Brownian tree introduced by Aldous and the associated Q-process which consists in an infinite spine on which are grafted independent Brownian trees. We present a reversal procedure on these trees that consists in looking at the tree downward from its top: the branching points becoming leaves and leaves becoming branching points. We prove that the distribution of this tree is invariant under this reversal procedure, which provides a better understanding of previous results from Bi and Delmas (2016).",

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AB - We consider the Brownian tree introduced by Aldous and the associated Q-process which consists in an infinite spine on which are grafted independent Brownian trees. We present a reversal procedure on these trees that consists in looking at the tree downward from its top: the branching points becoming leaves and leaves becoming branching points. We prove that the distribution of this tree is invariant under this reversal procedure, which provides a better understanding of previous results from Bi and Delmas (2016).

KW - Genealogical trees

KW - Real trees

KW - Stationary branching processes

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Reversal property of the Brownian tree

Abstract

Keywords

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