arXiv Analytics

Sign in

arXiv:2206.10496 [math.FA]AbstractReferencesReviewsResources

Convex subsets of non-convex Lorentz balls

Daniel J. Fresen

Published 2022-06-21Version 1

Many star bodies have convex subsets with approximately the same Gaussian measure (of the complement). Inspired by this phenomenon, and in connection with the randomized Dvoretzky theorem for Lorentz spaces, we derive bounds on the distribution of certain functions of a Gaussian random vector by approximating their sub-level sets by convex subsets.

Comments: 18 pages. Most of the material here was originally part of arXiv:2104.11974 and now stands as a paper on its own
Categories: math.FA, math.PR
Subjects: 52A27, 52A30, 60E05, 60E15
Related articles: Most relevant | Search more
arXiv:1601.02925 [math.FA] (Published 2016-01-12)
Sharp Poincaré-type inequality for the Gaussian measure on the boundary of convex sets
arXiv:1609.02205 [math.FA] (Published 2016-09-07)
On the Determination of Star Bodies from Their Half-Sections
arXiv:math/0602540 [math.FA] (Published 2006-02-24)
Generalized cosine transforms and classes of star bodies

Links

Toolbox