Date
2004
Notes
Journal électronique : http://www.math.washington.edu/~ejpecp/index.php
Dewey
Probabilités et mathématiques appliquées
Sujet
Probabilités
Journal issue
Electronic Journal of Probability
Volume
9
Number
paper 4
Publication date
2004
Article pages
57-97
Publisher
Institute of Mathematical Statistics
Author
Haas, Bénédicte
Miermont, Grégory
Type
Article accepté pour publication ou publié
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.