Tightness for branching random walk in a space-inhomogeneous random environment
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915041572290560 |
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| author | Kriechbaum, Xaver |
| author_facet | Kriechbaum, Xaver |
| contents | We consider the maximum $M_t$ of branching random walk in a space-inhomogeneous random environment on $\mathbb{Z}$. In this model the branching rate while at some location $x\in\mathbb{Z}$ is randomized in an i.i.d. manner. We prove that there is a centering $\widetilde{m}_t$ depending only on the environment such that $(M_t-\widetilde{m}_t)_{t\ge 0}$ is tight in an annealed sense. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01555 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tightness for branching random walk in a space-inhomogeneous random environment Kriechbaum, Xaver Probability 60J80 We consider the maximum $M_t$ of branching random walk in a space-inhomogeneous random environment on $\mathbb{Z}$. In this model the branching rate while at some location $x\in\mathbb{Z}$ is randomized in an i.i.d. manner. We prove that there is a centering $\widetilde{m}_t$ depending only on the environment such that $(M_t-\widetilde{m}_t)_{t\ge 0}$ is tight in an annealed sense. |
| title | Tightness for branching random walk in a space-inhomogeneous random environment |
| topic | Probability 60J80 |
| url | https://arxiv.org/abs/2408.01555 |