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arXiv · 1709.03610

Profile of a self-similar growth-fragmentation

François G. Ged
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Abstract

A self-similar growth-fragmentation describes the evolution of particles that grow and split as time passes. Its genealogy yields a self-similar continuum tree endowed with an intrinsic measure. Extending results of Haas for pure fragmentations, we relate the existence of an absolutely continuous profile to a simple condition in terms of the index of self-similarity and the so-called cumulant of the growth-fragmentation. When absolutely continuous, we approximate the profile by a function of the small fragments, and compute the Hausdorff dimension in the singular case. Applications to Boltzmann random planar maps are emphasized, exploiting recently established connections between growth-fragmentations and random maps by Bertoin et al.

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François G. Ged. 2017-09-11. Profile of a self-similar growth-fragmentation. https://arxiv.org/abs/1709.03610

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