On lipschitz embedding of finite metric spaces in Hilbert space Export

@article{citeulike:3078497, abstract = {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.}, author = {Bourgain, J.}, citeulike-article-id = {3078497}, citeulike-linkout-0 = {http://dx.doi.org/10.1007/BF02776078}, day = {12}, doi = {10.1007/BF02776078}, journal = {Israel Journal of Mathematics}, keywords = {embeddings, lipschitz, metric}, month = {March}, number = {1}, pages = {46--52}, posted-at = {2008-08-03 14:44:51}, priority = {2}, title = {On lipschitz embedding of finite metric spaces in Hilbert space}, url = {http://dx.doi.org/10.1007/BF02776078}, volume = {52}, year = {1985} }

TY - JOUR ID - citeulike:3078497 L3 - citeulike-article-id:3078497 N2 - 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. IS - 1 JF - Israel Journal of Mathematics EP - 52 TI - On lipschitz embedding of finite metric spaces in Hilbert space VL - 52 SP - 46 KW - embeddings KW - lipschitz KW - metric AU - Bourgain, J PY - 1985/03/12/ UR - http://dx.doi.org/10.1007/BF02776078 ER -