On lipschitz embedding of finite metric spaces in Hilbert space

  title={On lipschitz embedding of finite metric spaces in Hilbert space},
  author={J. Bourgain},
  journal={Israel Journal of Mathematics},
  • J. Bourgain
  • Published 1985
  • Mathematics
  • Israel Journal of Mathematics
  • 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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