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General Fragmentation Trees

Stephenson, Robin (2013), General Fragmentation Trees, Electronic Journal of Probability, 18, p. art 101. http://dx.doi.org/10.1214/EJP.v18-2703

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00805231
Date
2013
Journal name
Electronic Journal of Probability
Volume
18
Pages
art 101
Publication identifier
Metadata
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Author(s)
Stephenson, Robin
Abstract (EN)
We show that the genealogy of any self-similar fragmentation process can be encoded in a compact measured real tree. Under some Malthusian hypotheses, we compute the fractal Hausdorff dimension of this tree through the use of a natural measure on the set of its leaves. This generalizes previous work of Haas and Miermont which was restricted to conservative fragmentation processes.
Subjects / Keywords
Hausdorff dimension; self-similar fragmentations; continuum random trees; fragmentation trees