Scaling limit of the random walk on a Galton-Watson tree with regular varying offspring distribution

2023/09/17 by Qian, Dongjian, Xiao, Yang
#60F17 #60G50 #60J80 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2309.09200

Abstract

We consider a random walk on a Galton-Watson tree whose offspring distribution has a regular varying tail of order κ∈ (1,2). We prove the convergence of the renormalised height function of the walk towards the continuous-time height process of a spectrally positive strictly stable Lévy process, jointly with the convergence of the renormalised trace of the walk towards the continuum tree coded by the latter continuous-time height process.

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