On scaling limits of multitype Galton-Watson trees with possibly infinite variance



Berzunza, Gabriel
(2016) On scaling limits of multitype Galton-Watson trees with possibly infinite variance. Latin American Journal of Probability and Mathematical Statistics, 15 (1). p. 21.

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Abstract

In this work, we study asymptotics of multitype Galton-Watson trees with finitely many types. We consider critical and irreducible offspring distributions such that they belong to the domain of attraction of a stable law, where the stability indices may differ. We show that after a proper rescaling, their corresponding height process converges to the continuous-time height process associated with a strictly stable spectrally positive L\'evy process. This gives an analogue of a result obtained by Miermont in the case of multitype Galton-Watson trees with finite covariance matrices of the offspring distribution. Our approach relies on a remarkable decomposition for multitype trees into monotype trees introduced by Miermont.

Item Type: Article
Additional Information: 30 pages, 2 figures
Uncontrolled Keywords: math.PR, math.PR
Divisions: Faculty of Science and Engineering > School of Physical Sciences
Depositing User: Symplectic Admin
Date Deposited: 08 Jul 2021 07:59
Last Modified: 18 Jan 2023 21:36
DOI: 10.30757/alea.v15-02
Open Access URL: https://doi.org/10.30757/alea.v15-02
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3129190