Branching Random Walks, Stable Point Processes and Regular Variation
  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. 
Ayan Bhattacharya, Rajat Subhra Hazra and Parthanil Roy
math.PR