Extremes of multitype branching random walks: Heaviest tail wins

We consider a branching random walk on a multi(Q)-type, supercritical Galton-Watson tree which satisfies Kesten-Stigum condition. We assume that the displacements associated with the particles of type Q have regularly varying tails of index α, while the other types of particles have lighter tails than that of particles of type Q. In this article, we derive the weak limit of the sequence of point processes associated with the positions of the particles in the nth generation. We verify that the limiting point process is a randomly scaled scale-decorated Poisson point process (SScDPPP) using the tools developed in \cite{bhattacharya:hazra:roy:2016}. As a consequence, we shall obtain the asymptotic distribution of the position of the rightmost particle in the nth generation.

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article Extremes of multitype branching random walks: Heaviest tail wins A. Bhattacharya (Ayan), K. Maulik (Krishanu), Z. Palmowski (Zbigniew) and P. Roy (Parthanil)