English

Spherical Covariance Representations

Probability 2024-03-29 v1

Abstract

Covariance representations are developed for the uniform distributions on the Euclidean spheres in terms of spherical gradients and Hessians. They are applied to derive a number of Sobolev type inequalities and to recover and refine the concentration of measure phenomenon, including second order concentration inequalities. A detail account is also given in the case of the circle, with a short overview of H\"offding's kernels and covariance identities in the class of periodic functions.

Keywords

Cite

@article{arxiv.2403.19089,
  title  = {Spherical Covariance Representations},
  author = {Sergey G. Bobkov and Devraj Duggal},
  journal= {arXiv preprint arXiv:2403.19089},
  year   = {2024}
}
R2 v1 2026-06-28T15:36:32.781Z