Israel Journal of Mathematics

, Volume 102, Issue 1, pp 189–197

On embedding expanders into ℓ p spaces

Authors

    • Department of Applied MathematicsCharles University
Article

DOI: 10.1007/BF02773799

Cite this article as:
Matoušek, J. Isr. J. Math. (1997) 102: 189. doi:10.1007/BF02773799

Abstract

In this note we show that the minimum distortion required to embed alln-point metric spaces into the Banach space ℓ p is between (c 1/p) logn and (c 2/p) logn, wherec 2>c 1>0 are absolute constants and 1≤p<logn. The lower bound is obtained by a generalization of a method of Linial et al. [LLR95], by showing that constant-degree expanders (considered as metric spaces) cannot be embedded any better.

Copyright information

© The Magnes Press · The Hebrew University · Jerusalem 1997