A phase transition for the heights of a fragmentation tree |
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| Authors: | Adrien Joseph |
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| Affiliation: | Laboratoire de Probabilités et Modèles Aléatoires, Université Pierre et Marie Curie, 4 place Jussieu, 75005 Paris, France |
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| Abstract: | We provide information about the asymptotic regimes for a homogeneous fragmentation of a finite set. We establish a phase transition for the asymptotic behavior 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. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 39, 247‐274, 2011 |
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| Keywords: | occupancy scheme multiplicative cascade random split tree homogeneous fragmentation branching random walk |
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