Point process convergence for branching random walks with regularly varying steps

Ayan Bhattacharya; Rajat Subhra Hazra; Parthanil Roy

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arXiv · 1411.5646

Point process convergence for branching random walks with regularly varying steps

Ayan Bhattacharya·Rajat Subhra Hazra·Parthanil Roy

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Abstract

We consider the limiting behaviour of the point processes associated with a branching random walk with supercritical branching mechanism and balanced regularly varying step size. Assuming that the underlying branching process satisfies Kesten-Stigum condition, it is shown that the point process sequence of properly scaled displacements coming from the n-th generation converges weakly to a Cox cluster process. In particular, we establish that a conjecture of Brunet and Derrida (2011) remains valid in this setup, investigate various other issues mentioned in their paper and recover the main result of Durrett (1983) in our framework.

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Ayan Bhattacharya, Rajat Subhra Hazra, Parthanil Roy. 2014-11-20. Point process convergence for branching random walks with regularly varying steps. https://arxiv.org/abs/1411.5646

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