A phase transition for the heights of a fragmentation tree

Adrien Joseph (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We provide information about the asymptotic regimes for a homogeneous fragmentation of a finite set. We establish a phase transition for the asymptotic behaviours of the shattering times, defined as the first instants when all the blocks of the partition process have cardinality less than a fixed integer. Our results may be applied to the study of certain random split trees.

Mots clés: branching random walk; occupancy scheme; multiplicative cascade; random split tree; homogeneous fragmentation; branching random walk.

Domaines: Probabilités [math.PR]

Adrien Joseph. A phase transition for the heights of a fragmentation tree. 2009. ⟨hal-00386468⟩