Lipschitz correspondence between metric measure spaces and random distance matrices

Details Lipschitz correspondence between metric measure spaces and random distance matrices Lipschitz correspondence between metric measure spaces and random distance matrices

2011-10-28

arxiv.org/abs/1110.6333v1

Mathematics

Probability

15 pages

Scientific paper

Given a metric space with a Borel probability measure, for each integer $N$ we obtain a probability distribution on $N\times N$ distance matrices by considering the distances between pairs of points in a sample consisting of $N$ points chosen indepenedently from the metric space with respect to the given measure. We show that this gives an asymptotically bi-Lipschitz relation between metric measure spaces and the corresponding distance matrices. This is an effective version of a result of Vershik that metric measure spaces are determined by associated distributions on infinite random matrices.

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