The extremal process of two-speed branching random walk
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917948412657664 |
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| author | Luo, Lianghui |
| author_facet | Luo, Lianghui |
| contents | 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]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_05994 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The extremal process of two-speed branching random walk Luo, Lianghui Probability 60F05, 60G70, 60J80 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]. |
| title | The extremal process of two-speed branching random walk |
| topic | Probability 60F05, 60G70, 60J80 |
| url | https://arxiv.org/abs/2503.05994 |