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arXiv · 2507.08692

Some notes on higher order concentration of measure

Holger Sambale
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Abstract

This survey-type paper provides a common framework for a larger number of higher order concentration results (i.\,e., concentration results for non-Lipschitz functions which have bounded derivatives of higher order) in the spirit of Bobkov--G\"otze--Sambale (2019). Situations inlude measures satisfying various functional inequalities (log-Sobolev, Poincar\'{e}, $\mathrm{LS}_q$), uniform and cone measures on spheres with respect to the Euclidean as well as $\ell_p^n$-norms, Stiefel and Grassmann manifolds as well as discrete situations. In particular in the latter case, some open questions and remarks are stated.

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Holger Sambale. 2025-07-11. Some notes on higher order concentration of measure. https://arxiv.org/abs/2507.08692

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