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 |
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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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