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arXiv · 1605.04810

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

Gabriel Berzunza
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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 Lévy 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.

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Gabriel Berzunza. 2016-07-19. On scaling limits of multitype Galton-Watson trees with possibly infinite variance. https://arxiv.org/abs/1605.04810

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