The max-type quasimetrics on probability simplices
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914126919368704 |
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| author | Eckstein, Michał Miller, Tomasz Życzkowski, Karol |
| author_facet | Eckstein, Michał Miller, Tomasz Życzkowski, Karol |
| contents | Quasimetric spaces form a natural framework to study distance problems with an inherent directional asymmetry. We introduce a simple novel class of quasimetrics on probability simplices, inspired by the Chebyshev distance. It is shown that such quasimetrics have expedient geometric properties -- they induce the Euclidean topology and a Finslerian infinitesimal structure, with which the probability simplices become geodesic spaces. Moreover, we prove that the broad family of the proposed quasimetrics are monotone under bistochastic maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_27368 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The max-type quasimetrics on probability simplices Eckstein, Michał Miller, Tomasz Życzkowski, Karol Metric Geometry Mathematical Physics 53B40, 53B12, 51F99 Quasimetric spaces form a natural framework to study distance problems with an inherent directional asymmetry. We introduce a simple novel class of quasimetrics on probability simplices, inspired by the Chebyshev distance. It is shown that such quasimetrics have expedient geometric properties -- they induce the Euclidean topology and a Finslerian infinitesimal structure, with which the probability simplices become geodesic spaces. Moreover, we prove that the broad family of the proposed quasimetrics are monotone under bistochastic maps. |
| title | The max-type quasimetrics on probability simplices |
| topic | Metric Geometry Mathematical Physics 53B40, 53B12, 51F99 |
| url | https://arxiv.org/abs/2510.27368 |