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Texas A&M University
Mathematics

Events for 07/20/2016 from all calendars

Workshop in Analysis and Probability Seminar

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Time: 2:00PM - 2:50PM

Location: BLOC 220

Speaker: Susanna Dann, Vienna University of Technology

Title: Bounding marginal densities via affine isoperimetry

Abstract: Let $\mu$ be a probability measure on $\R^n$ with a bounded density $f$. We prove that the marginals of $f$ on most subspaces are well-bounded. For product measures, studied recently by Rudelson and Vershynin, our results show there is a trade-off between the strength of such bounds and the probability with which they hold. Our proof rests on new affinely-invariant extremal inequalities for certain averages of $f$ on the Grassmannian and affine Grassmannian. These are motivated by Lutwak's dual affine quermassintegrals for convex sets. We show that key invariance properties of the latter, due to Grinberg, extend to families of functions. The inequalities we obtain can be viewed as functional analogues of results due to Busemann--Straus, Grinberg and Schneider.