Spherical Covariance Representations

2024/03/28 by Bobkov, Sergey G., Duggal, Devraj
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2403.19089

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 Höffding's kernels and covariance identities in the class of periodic functions.

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