Lipschitz Correspondence between Metric Measure Spaces and Random Distance Matrices

Gadgil, Siddhartha and Krishnapur, Manjunath (2013) Lipschitz Correspondence between Metric Measure Spaces and Random Distance Matrices. In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES (24). pp. 5623-5644.

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Abstract

Given a metric space with a Borel probability measure, for each integer N, we obtain a probability distribution on N x N distance matrices by considering the distances between pairs of points in a sample consisting of N points chosen independently 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.

Item Type:	Journal Article
Publication:	INTERNATIONAL MATHEMATICS RESEARCH NOTICES
Publisher:	OXFORD UNIV PRESS
Additional Information:	copyright for this article belongs to OXFORD UNIV PRESS,ENGLAND
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	13 Jan 2014 06:34
Last Modified:	13 Jan 2014 06:34
URI:	http://eprints.iisc.ac.in/id/eprint/48187

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