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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.27368 |
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Table of 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.