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.
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 |
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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 |