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Volume properties of high-dimensional Orlicz balls
Franck Barthe</name> <arxiv:affiliation>IMT</arxiv:affilia · 2021-06-03 · via math.PR updates on arXiv.org

We prove asymptotic estimates for the volume of families of Orlicz balls in high dimensions. As an application, we describe a large family of Orlicz balls which verify a famous conjecture of Kannan, Lov{á}sz and Simonovits about spectral gaps. We also study the asymptotic independence of coordinates on uniform random vectors on Orlicz balls, as well as integrability properties of their linear functionals.

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