On sharp bounds for marginal densities of product measures
| Autor: | Galyna V. Livshyts, Grigoris Paouris, Peter Pivovarov |
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| Rok vydání: | 2016 |
| Předmět: |
General Mathematics
Probability (math.PR) 010102 general mathematics Probability density function 01 natural sciences Combinatorics 010104 statistics & probability Bounded function FOS: Mathematics Ball (mathematics) Affine transformation 0101 mathematics Isoperimetric inequality Mathematics - Probability Mathematics |
| Zdroj: | Israel Journal of Mathematics. 216:877-889 |
| ISSN: | 1565-8511 0021-2172 |
| DOI: | 10.1007/s11856-016-1431-5 |
| Popis: | We discuss optimal constants in a recent result of Rudelson and Vershynin on marginal densities. We show that if f is a probability density on R n of the form f(x) = П =1 f i (x i ), where each f i is a density on R, say bounded by one, then the density of any marginal π E (f) is bounded by 2 k/2, where k is the dimension of E. The proof relies on an adaptation of Ball’s approach to cube slicing, carried out for functions. Motivated by inequalities for dual affine quermassintegrals, we also prove an isoperimetric inequality for certain averages of the marginals of such f for which the cube is the extremal case. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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