General Fragmentation Trees

Robin Stephenson (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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.

Mots clés: fragmentation trees; continuum random trees; self-similar fragmentations; Hausdorff dimension

Domaines: Probabilités [math.PR]

Robin Stephenson. General Fragmentation Trees. Electronic Journal of Probability, 2013, 18 (101), pp.1-45. ⟨10.1214/EJP.v18-2703⟩. ⟨hal-00805231v2⟩