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A Benamou-Brenier formula for transport distances between stationary random measures

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arxiv 2402.04842 v1 pith:YMOD2AHY submitted 2024-02-07 math.PR

Martin Huesmann , Bastian Müller This is my paper · ORCID
classification math.PR
keywords benamou-breniermathsfmeasuresmetricrandomstationaryderivedistances
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abstract

We derive a Benamou-Brenier type dynamical formulation for the Wasserstein metric $\mathsf W_p$ between stationary random measures recently introduced in [EHJM23]. A key step is a reformulation of the metric $\mathsf W_p$ using Palm probabilities.

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  1. Pyramids and Extended Metric Measure Spaces

    math.MG 2026-07 conditional novelty 8.0 of 10

    Every pyramid of metric measure spaces can be realized as the □-closure of the pyramid associated with an extended metric measure space, and concentrated pyramids have a unique representation.

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