• DOI:10.1007/BF02776078
Corpus ID: 121649019

On lipschitz embedding of finite metric spaces in Hilbert space

@article{Bourgain1985OnLE,
  title={On lipschitz embedding of finite metric spaces in Hilbert space},
  author={J. Bourgain},
  journal={Israel Journal of Mathematics},
  year={1985},
  volume={52},
  pages={46-52}
}

J. Bourgain

Published 1985

Mathematics

Israel Journal of Mathematics

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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.