Nonembeddability theorems via Fourier analysis

Subhash Khot; Assaf Naor

Nonembeddability theorems via Fourier analysis

Functional Analysis 2007-05-23 v1 Metric Geometry

Authors: Subhash Khot , 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.

Keywords

fourier analysis fourier restriction estimates distance sets

Cite

@article{arxiv.math/0510547,
  title  = {Nonembeddability theorems via Fourier analysis},
  author = {Subhash Khot and Assaf Naor},
  journal= {arXiv preprint arXiv:math/0510547},
  year   = {2007}
}

Comments

With an appendix on quantitative estimates in Bourgain's noise sensitivity theorem. To appear in Mathematiche Annalen. An extended abstract appeared in FOCS 2005

Nonembeddability theorems via Fourier analysis

Abstract

Keywords

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