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On embedding expanders into ℓ p spaces

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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.

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Authors and Affiliations

  1. Department of Applied Mathematics, Charles University, Malostranské nám. 25, 118 00, Praha 1, Czech Republic

    Jiří Matoušek

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  1. Jiří Matoušek
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Correspondence to Jiří Matoušek.

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Research supported by Czech Republic Grant GAČR 201/94/2167 and Charles University grants No. 351 and 361.

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Matoušek, J. On embedding expanders into ℓ p spaces. Isr. J. Math. 102, 189–197 (1997). https://doi.org/10.1007/BF02773799

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