Spherical Covariance Representations

Sergey G. Bobkov; Devraj Duggal

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arXiv · 2403.19089

Spherical Covariance Representations

Sergey G. Bobkov·Devraj Duggal

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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.

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Sergey G. Bobkov, Devraj Duggal. 2024-03-28. Spherical Covariance Representations. https://arxiv.org/abs/2403.19089

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