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The Genealogy of Self-similar Fragmentations with Negative Index as a Continuum Random Tree


 
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1. Title Title of document The Genealogy of Self-similar Fragmentations with Negative Index as a Continuum Random Tree
 
2. Creator Author's name, affiliation, country Bénédicte Haas; Université Pierre et Marie Curie
 
2. Creator Author's name, affiliation, country Grégory Miermont; DMA, Ecole Normale Supérieure, et Université Paris VI
 
3. Subject Discipline(s)
 
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4. Description Abstract 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 Hausdorff dimensions of these trees, and the maximal Hölder exponents of the height functions.
 
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7. Date (YYYY-MM-DD) 2004-02-13
 
8. Type Status & genre Peer-reviewed Article
 
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9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/187
 
10. Identifier Digital Object Identifier 10.1214/EJP.v9-187
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 9
 
12. Language English=en
 
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