A quantitative central limit theorem for Poisson horospheres in high dimensions
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910356476002304 |
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| author | Kabluchko, Zakhar Rosen, Daniel Thäle, Christoph |
| author_facet | Kabluchko, Zakhar Rosen, Daniel Thäle, Christoph |
| contents | Consider a stationary Poisson process of horospheres in a $d$-dimensional hyperbolic space. In the focus of this note is the total surface area these random horospheres induce in a sequence of balls of growing radius $R$. The main result is a quantitative, non-standard central limit theorem for these random variables as the radius $R$ of the balls and the space dimension $d$ tend to infinity simultaneously. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_17827 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A quantitative central limit theorem for Poisson horospheres in high dimensions Kabluchko, Zakhar Rosen, Daniel Thäle, Christoph Probability Metric Geometry 52A55, 60D05 (Primary), 60F05, 60G55 (Secondary) Consider a stationary Poisson process of horospheres in a $d$-dimensional hyperbolic space. In the focus of this note is the total surface area these random horospheres induce in a sequence of balls of growing radius $R$. The main result is a quantitative, non-standard central limit theorem for these random variables as the radius $R$ of the balls and the space dimension $d$ tend to infinity simultaneously. |
| title | A quantitative central limit theorem for Poisson horospheres in high dimensions |
| topic | Probability Metric Geometry 52A55, 60D05 (Primary), 60F05, 60G55 (Secondary) |
| url | https://arxiv.org/abs/2303.17827 |