Gaussian width bounds with applications to arithmetic progressions in random settings

@article{Brit2017GaussianWB,
  title={Gaussian width bounds with applications to arithmetic progressions in random settings},
  author={J. Bri{\"e}t and Sivakanth Gopi},
  journal={ArXiv},
  year={2017},
  volume={abs/1711.05624}
}
  • J. Briët, Sivakanth Gopi
  • Published 2017
  • Mathematics, Computer Science
  • ArXiv
  • Motivated by two problems on arithmetic progressions (APs)—concerning large deviations for AP counts in random sets and random differences in Szemer´edi’s theorem— we prove upper bounds on the Gaussian width of the image of the n-dimensional Boolean hypercube under a mapping ψ : Rn → Rk, where each coordinate is a constant-degree multilinear polynomial with 0/1 coefficients. We show the following applications of our bounds. Let [Z/NZ]p be the random subset of Z/NZ containing each element… CONTINUE READING
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