Reversal property of the Brownian tree
Probability
2017-10-11 v1
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).
Cite
@article{arxiv.1710.03460,
title = {Reversal property of the Brownian tree},
author = {Romain Abraham and Jean-Francois Delmas},
journal= {arXiv preprint arXiv:1710.03460},
year = {2017}
}
Comments
This is the second version of the preprint arXiv:1612.03715 that has been splitted into two papers