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The extremal process of two-speed branching random walk

Probability 2025-03-11 v1

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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Cite

@article{arxiv.2503.05994,
  title  = {The extremal process of two-speed branching random walk},
  author = {Lianghui Luo},
  journal= {arXiv preprint arXiv:2503.05994},
  year   = {2025}
}

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28 pages