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The genealogy of self-similar fragmentations with negative index as a continuum random tree

Haas, Bénédicte; Miermont, Grégory (2004), The genealogy of self-similar fragmentations with negative index as a continuum random tree, Electronic Journal of Probability, 9, paper 4, p. 57-97

Type
Article accepté pour publication ou publié
Date
2004
Journal name
Electronic Journal of Probability
Volume
9
Number
paper 4
Publisher
Institute of Mathematical Statistics
Pages
57-97
Metadata
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Author(s)
Haas, Bénédicte
Miermont, Grégory
Abstract (EN)
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 which belongs to the family of Continuum Random Trees of Aldous. When the splitting times of the fragmentation are dense near 0, the tree can in turn be encoded into a continuous height function, just as the Brownian Continuum Random Tree is encoded in a normalized Brownian excursion. Under mild hypotheses, we then compute the Hausdor® dimensions of these trees, and the maximal HÄ older exponents of the height functions.
Subjects / Keywords
Probabilités