Israel Journal of Mathematics

, Volume 52, Issue 1–2, pp 46–52 | Cite as

On lipschitz embedding of finite metric spaces in Hilbert space

  • J. Bourgain
Article

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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    J. Bourgain, V. Milman and H. Wolfson,Theorie of type in finite metric spaces, Trans. Am. Math. Soc., to appear.Google Scholar
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    W. Johnson and J. Lindenstrauss,Extensions of Lipschitz mappings into a Hilbert space, Contemp. Math.26 (1984), 189–206.MATHMathSciNetGoogle Scholar
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    J. Lindenstrauss, Proceedings Missouri Conf., Missouri — Columbia (1984), to appear.Google Scholar
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Copyright information

© The Weizmann Science Press of Israel 1985

Authors and Affiliations

  • J. Bourgain
    • 1
  1. 1.Department of MathematicsVrije Universiteit BrusselBrusselsBelgium

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