Left Tail of the Subcritical Derivative Martingale in a Branching Wiener Process
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916902741213184 |
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| author | Chen, Xinxin Huang, Yichao Ma, Heng |
| author_facet | Chen, Xinxin Huang, Yichao Ma, Heng |
| contents | We establish a rather sharp two-side estimate for the tail probability of the derivative martingale limit in a branching random walk throughout the entire subcritical regime, confirming a conjecture by Lacoin, Rhodes, and Vargas (\emph{Duke Math. J.} 171(3):483--545, 2022.) for the special case of log-correlated Gaussian fields on trees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_11983 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Left Tail of the Subcritical Derivative Martingale in a Branching Wiener Process Chen, Xinxin Huang, Yichao Ma, Heng Probability We establish a rather sharp two-side estimate for the tail probability of the derivative martingale limit in a branching random walk throughout the entire subcritical regime, confirming a conjecture by Lacoin, Rhodes, and Vargas (\emph{Duke Math. J.} 171(3):483--545, 2022.) for the special case of log-correlated Gaussian fields on trees. |
| title | Left Tail of the Subcritical Derivative Martingale in a Branching Wiener Process |
| topic | Probability |
| url | https://arxiv.org/abs/2508.11983 |