Lipschitz Correspondence between Metric Measure Spaces and Random Distance Matrices
Data(s) |
2013
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Resumo |
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. |
Formato |
application/pdf |
Identificador |
http://eprints.iisc.ernet.in/48187/1/Int_Mat_Res_Not_24_5623_2013.pdf 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. |
Publicador |
OXFORD UNIV PRESS |
Relação |
http://dx.doi.org/10.1093/imrn/rns208 http://eprints.iisc.ernet.in/48187/ |
Palavras-Chave | #Mathematics |
Tipo |
Journal Article PeerReviewed |