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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 the tree is invariant under this reversal procedure, which provides a better understanding of previous results from Bi and Delmas (2016).
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Contributor : Romain Abraham <>
Submitted on : Tuesday, October 10, 2017 - 10:59:29 AM
Last modification on : Tuesday, December 8, 2020 - 10:09:24 AM
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  • HAL Id : hal-01613842, version 1



Romain Abraham, Jean-François Delmas. Reversal property of the Brownian tree. ALEA : Latin American Journal of Probability and Mathematical Statistics, Instituto Nacional de Matemática Pura e Aplicada, 2018, 15, pp.1293-1309. ⟨hal-01613842⟩



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