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}
}