Reversal property of the Brownian tree

This is the second version of the preprint "Reversal properties and exact simulation of the genealogical tree for a stationary branching population" that has been splitted into two papers.International audienceWe 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)