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On the Gromov-Prohorov distance

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arxiv 2005.13505 v2 pith:TUAH767P submitted 2020-05-27 math.PR

Svante Janson This is my paper · ORCID
classification math.PR
keywords distancegromov-prohorovconvergenceresultsarraybasicclaimdefinitions
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We survey some basic results on the Gromov-Prohorov distance between metric measure spaces. (We do not claim any new results.) We give several different definitions and show the equivalence of them. We also show that convergence in the Gromov-Prohorov distance is equivalent to convergence in distribution of the array of distances between finite sets of random points.

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  1. Random punctured hyperbolic surfaces & the Brownian sphere

    math.PR 2025-08 conditional novelty 8.0 of 10

    Random Weil-Petersson punctured spheres converge, after fourth-root rescaling, to the Brownian sphere.

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