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math.PR2015
On sharp bounds for marginal densities of product measures
Galyna Livshyts, Grigoris Paouris, Peter Pivovarov
We discuss optimal constants in a recent result of Rudelson and Vershynin on marginal densities. We show that if is a probability density on of the form $f(x)=\prod_{i=1…
math.PR2015
On the Brunn-Minkowski inequality for general measures with applications to new isoperimetric-type inequalities
Galyna Livshyts, Arnaud Marsiglietti, Piotr Nayar +1
In this paper we present new versions of the classical Brunn-Minkowski inequality for different classes of measures and sets. We show that the inequality \[ μ(λA + (1-λ)B)^{1/n} \g…