Upper moderate deviation probabilities for the maximum of branching Brownian motion
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908639571214336 |
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| author | Chataignier, Louis |
| author_facet | Chataignier, Louis |
| contents | It is known from Bramson (1983) that the maximum of branching Brownian motion at time $t$ is asymptotically around an explicit function $m_t$, which involves a first ballistic order and a logarithmic correction. In this paper, we give an asymptotic equivalent for its upper moderate deviation probability, that is, the probability that the maximum achieves $m_t + x_t$ at time $t$, where $1 \ll x_t \ll t$. We adopt a probabilistic approach that employs a modified version of the second moment method. As a byproduct, we obtain information about the typical behavior of particles contributing to such deviations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_11363 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Upper moderate deviation probabilities for the maximum of branching Brownian motion Chataignier, Louis Probability 60J80, 60F10 It is known from Bramson (1983) that the maximum of branching Brownian motion at time $t$ is asymptotically around an explicit function $m_t$, which involves a first ballistic order and a logarithmic correction. In this paper, we give an asymptotic equivalent for its upper moderate deviation probability, that is, the probability that the maximum achieves $m_t + x_t$ at time $t$, where $1 \ll x_t \ll t$. We adopt a probabilistic approach that employs a modified version of the second moment method. As a byproduct, we obtain information about the typical behavior of particles contributing to such deviations. |
| title | Upper moderate deviation probabilities for the maximum of branching Brownian motion |
| topic | Probability 60J80, 60F10 |
| url | https://arxiv.org/abs/2505.11363 |