Nonembeddability theorems via Fourier analysis

Subhash Khot; Assaf Naor

Nonembeddability theorems via Fourier analysis

泛函分析 2007-05-23 v1 度量几何

作者: Subhash Khot , Assaf Naor

摘要

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.

关键词

fourier analysis fourier restriction estimates distance sets

引用

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

备注

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

摘要

关键词

引用

备注

相关论文