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arXiv · 2503.05994

The extremal process of two-speed branching random walk

Lianghui Luo
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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].

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Lianghui Luo. 2025-03-08. The extremal process of two-speed branching random walk. https://arxiv.org/abs/2503.05994

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