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General fragmentation trees. (English) Zbl 1297.60023

Author’s abstract: 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 B. Haas and G. Miermont [Electron. J. Probab. 9, Paper No. 4, 57–97 (2004; Zbl 1064.60076)] which was restricted to conservative fragmentation processes.

MSC:

60G18 Self-similar stochastic processes
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60G57 Random measures
60G60 Random fields
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)

Citations:

Zbl 1064.60076
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