Mathematics – Probability
Scientific paper
2004-01-05
Electronic Journal of Probability 9 (2004) 57-97
Mathematics
Probability
Scientific paper
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 H\"older exponents of the height functions.
Haas Bénédicte
Miermont Grégory
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