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Fragmentation of compositions and intervals

By Anne-Laure Basdevant

Abstract

The fragmentation processes of exchangeable partitions have already been studied by several authors. In this paper, we examine rather fragmentation of exchangeable compositions, that means partitions of $\mathbb{N}$ where the order of the blocks counts. We will prove that such a fragmentation is bijectively associated to an interval fragmentation. Using this correspondence, we then calculate the Hausdorff dimension of certain random closed set that arise in interval fragmentations and we study Ruelle's interval fragmentation

Topics: interval fragmentation, exchangeable compositions, AMS 60J25 60G09, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR]
Publisher: HAL CCSD
Year: 2005
OAI identifier: oai:HAL:hal-00013926v2
Provided by: Hal-Diderot
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