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math.PR2004★ 83 cited
Self-similar fragmentations derived from the stable tree II: splitting at nodes
Gregory Marc Miermont
We study a natural fragmentation process of the so-called stable tree introduced by Duquesne and Le Gall, which consists in removing the nodes of the tree according to a certain pr…
math.PR2004★ 41 cited
The exploration process of inhomogeneous continuum random trees, and an extension of Jeulin's local time identity
David J Aldous, Gregory Miermont, Jim Pitman
We study the inhomogeneous continuum random trees (ICRT) that arise as weak limits of birthday trees. We give a description of the exploration process, a function defined on [0,1]…
math.PR2004
The genealogy of self-similar fragmentations with negative index as a continuum random tree
Benedicte Haas, Gregory Miermont
We encode a certain class of stochastic fragmentation processes, namely self-similar fragmentation processes with a negative index of self-similarity, into a metric family tree whi…