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On lipschitz embedding of finite metric spaces in Hilbert space - Israel Journal of Mathematics

  • ️Bourgain, J.
  • ️Fri Mar 01 1985

Abstract

It is shown that anyn point metric space is up to logn lipeomorphic to a subset of Hilbert space. We also exhibit an example of ann point metric space which cannot be embedded in Hilbert space with distortion less than (logn)/(log logn), showing that the positive result is essentially best possible. The methods used are of probabilistic nature. For instance, to construct our example, we make use of random graphs.

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References

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Authors and Affiliations

  1. Department of Mathematics, Vrije Universiteit Brussel, Pleinlaan 2, 10F7, 1050, Brussels, Belgium

    J. Bourgain

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  1. J. Bourgain

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Bourgain, J. On lipschitz embedding of finite metric spaces in Hilbert space. Israel J. Math. 52, 46–52 (1985). https://doi.org/10.1007/BF02776078

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  • Received: 27 August 1984

  • Issue Date: March 1985

  • DOI: https://doi.org/10.1007/BF02776078

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