Point process convergence for branching random walks with regularly\n varying steps

2014/11/20 by Ayan Bhattacharya, Rajat Subhra Hazra, Bhattacharya, Ayan +3
Computer Science · Mathematics · #60G55 #Bayesian Methods and Mixture Models #FOS: Mathematics #Primary 60J70 #Probability (math.PR) #Random Matrices and Applications #Secondary 60J80 #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1411.5646

openalex publication_date 2014/11/20 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

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

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