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Profile of a self-similar growth-fragmentation


Ged, François Gaston (2019). Profile of a self-similar growth-fragmentation. Electronic Journal of Probability, 24:1-21.

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].

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].

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Statistics and Probability
Social Sciences & Humanities > Statistics, Probability and Uncertainty
Uncontrolled Keywords:Statistics, Probability and Uncertainty, Statistics and Probability
Language:English
Date:1 January 2019
Deposited On:09 Nov 2021 13:33
Last Modified:25 Jun 2024 01:46
Publisher:Institute of Mathematical Statistics
ISSN:1083-6489
OA Status:Gold
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1214/18-ejp253
  • Content: Published Version
  • Licence: Creative Commons: Attribution 3.0 Unported (CC BY 3.0)