Translator Disclaimer
2019 Profile of a self-similar growth-fragmentation
François Gaston Ged
Electron. J. Probab. 24: 1-21 (2019). DOI: 10.1214/18-EJP253

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 [13] 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 [1, 5].

Citation

Download Citation

François Gaston Ged. "Profile of a self-similar growth-fragmentation." Electron. J. Probab. 24 1 - 21, 2019. https://doi.org/10.1214/18-EJP253

Information

Received: 12 April 2018; Accepted: 3 December 2018; Published: 2019
First available in Project Euclid: 15 February 2019

zbMATH: 1412.60111
MathSciNet: MR3916327
Digital Object Identifier: 10.1214/18-EJP253

Subjects:
Primary: 60G18, 60G30, 60J25

JOURNAL ARTICLE
21 PAGES


SHARE
Vol.24 • 2019
Back to Top