Branching Random Walks, Stable Point Processes and Regular Variation
Probability
2016-01-27 v2
Abstract
Using the language of regular variation, we give a sufficient condition for a point process to be in the superposition domain of attraction of a strictly stable point process. This sufficient condition is then used to obtain an explicit representation of the weak limit of a sequence of point processes induced by a branching random walk with jointly regularly varying displacements. As a consequence, we extend the main result of Durrett (1983) and verify that two related predictions of Brunet and Derrida (2011) remain valid for this model.
Cite
@article{arxiv.1601.01656,
title = {Branching Random Walks, Stable Point Processes and Regular Variation},
author = {Ayan Bhattacharya and Rajat Subhra Hazra and Parthanil Roy},
journal= {arXiv preprint arXiv:1601.01656},
year = {2016}
}
Comments
30 pages. 2 figures. Typos fixed thanks to a detailed and careful reading by Frank den Hollander