vix.ing · top · new · best · stats · spec

The extremal process of two-speed branching random walk

2025/03/08 by Luo, Lianghui
#60F05 #60G70 #60J80 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2503.05994

Abstract

We consider a two-speed branching random walk, which consists of two macroscopic stages with different reproduction laws. We prove that the centered maximum converges in law to a Gumbel variable with a random shift and the extremal process converges in law to a randomly shifted decorated Poisson point process, which can be viewed as a discrete analog for the corresponding results for the two-speed branching Brownian motion, previously established by Bovier and Hartung [12].

Related