Extreme events and impact statistics for unipotent actions on the space of lattices
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917007968960512 |
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| author | Marklof, Jens Strömbergsson, Andreas Yu, Shucheng |
| author_facet | Marklof, Jens Strömbergsson, Andreas Yu, Shucheng |
| contents | This paper extends a recent extreme value law for horocycle flows on the space of two-dimensional lattices, due to Kirsebom and Mallahi-Karai, to the simplest examples of rank-$k$ unipotent actions on the space of $n$-dimensional lattices. We analyse the problem in terms of the hitting time and impact statistics for the unipotent action with respect to a shrinking surface of section, following the strategy of Pollicott and the first named author in the case of hyperbolic surfaces. If $k=n-1$, the limit law is given by directional statistics of Euclidean lattices, whilst for $k<n-1$ we observe new distributions for which we derive precise tail asymptotics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11371 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extreme events and impact statistics for unipotent actions on the space of lattices Marklof, Jens Strömbergsson, Andreas Yu, Shucheng Dynamical Systems Number Theory This paper extends a recent extreme value law for horocycle flows on the space of two-dimensional lattices, due to Kirsebom and Mallahi-Karai, to the simplest examples of rank-$k$ unipotent actions on the space of $n$-dimensional lattices. We analyse the problem in terms of the hitting time and impact statistics for the unipotent action with respect to a shrinking surface of section, following the strategy of Pollicott and the first named author in the case of hyperbolic surfaces. If $k=n-1$, the limit law is given by directional statistics of Euclidean lattices, whilst for $k<n-1$ we observe new distributions for which we derive precise tail asymptotics. |
| title | Extreme events and impact statistics for unipotent actions on the space of lattices |
| topic | Dynamical Systems Number Theory |
| url | https://arxiv.org/abs/2510.11371 |