Branching random walks, stable point processes and regular variation
vendredi 1 juillet 2016, 9h30 - 10h30
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.
This talk in based on a joint work with Ayan Bhattacharya and Rajat Subhra Hazra. The manuscript is available at http://arxiv.org/abs/1601.01656.