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
TypeArticle accepté pour publication ou publié
Journal nameElectronic Journal of Probability
Institute of Mathematical Statistics
MetadataShow full item record
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 / KeywordsProbabilités
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Winkel, Matthias; Pitman, Jim; Miermont, Grégory; Haas, Bénédicte (2008-09) Article accepté pour publication ou publié