Point process convergence for branching random walks with regularly varying steps
Annales de l'institut Henri Poincare (B) Probability and Statistics
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 nth generation converges weakly to a Cox cluster process. In particular, we establish that a conjecture of (J. Stat. Phys. 143 (3) (2011) 420-446) remains valid in this setup, investigate various other issues mentioned in their paper and recover the main result of (Z. Wahrsch. Verw. Gebiete 62 (2) (1983) 165-170) in our framework.
Bhattacharya, Ayan; Hazra, Rajat Subhra; and Roy, Parthanil, "Point process convergence for branching random walks with regularly varying steps" (2017). Journal Articles. 2584.