A phase transition for the heights of a fragmentation tree

2009/05/21 by Joseph, Adrien
#60F15 #60J80. #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.0905.3545

Abstract

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.

Related

• The size of random fragmentation trees
• Behavior near the extinction time in self-similar fragmentations I: the stable case
• The fragmentation process of an infinite recursive tree and\n Ornstein-Uhlenbeck type processes
• Trees within trees II: Nested Fragmentations
• Self-similar fragmentations derived from the stable tree I