Nonembeddability theorems via Fourier analysis

Details Nonembeddability theorems via Fourier analysis Nonembeddability theorems via Fourier analysis

2005-10-26

arxiv.org/abs/math/0510547v1

Mathematics

Functional Analysis

With an appendix on quantitative estimates in Bourgain's noise sensitivity theorem. To appear in Mathematiche Annalen. An exte

Scientific paper

Various new nonembeddability results (mainly into $L_1$) are proved via
Fourier analysis. In particular, it is shown that the Edit Distance on
$\{0,1\}^d$ has $L_1$ distortion $(\log d)^{\frac12-o(1)}$. We also give new
lower bounds on the $L_1$ distortion of flat tori, quotients of the discrete
hypercube under group actions, and the transportation cost (Earthmover) metric.

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