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arXiv · 2510.27368

The max-type quasimetrics on probability simplices

Michał Eckstein·Tomasz Miller·Karol Życzkowski
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Abstract

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.

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Michał Eckstein, Tomasz Miller, Karol Życzkowski. 2025-10-31. The max-type quasimetrics on probability simplices. https://arxiv.org/abs/2510.27368

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