This is an announcement for the paper "Nonembeddability theorems via Fourier analysis" by Subhash Khot and Assaf Naor.

Abstract: 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.

Archive classification: Functional Analysis; Metric Geometry

Mathematics Subject Classification: 46B20; 68U05

Remarks: With an appendix on quantitative estimates in Bourgain's noise

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/math.FA/0510547

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http://arXiv.org/abs/math.FA/0510547

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