Sharpened forms of the concentration of measure phenomenon for classes of functions on the sphere are developed in terms of Hessians of these functions.
Bibliographical noteFunding Information:
This research was partially supported by NSF Grant DMS-1612961, the Humboldt Foundation and SFB 701 at Bielefeld University. We would like to thank Michel Ledoux for the differential geometric motivation of Proposition 4.1, and Bo'az Klartag for the careful reading of the manuscript and valuable comments.
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- Concentration of measure phenomenon
- logarithmic Sobolev inequalities