4 citations · 6 across the 11 of their papers we have counts for
5 papers · 1 filter
A stochastic Prekopa-Leindler inequality for log-concave functions
Peter Pivovarov, Jesus Rebollo Bueno
The Brunn-Minkowski and Prékopa-Leindler inequalities admit a variety of proofs that are inspired by convexity. Nevertheless, the former holds for compact sets and the latter for i…
Randomized Urysohn-type inequalities
Thomas Hack, Peter Pivovarov
As a natural analog of Urysohn's inequality in Euclidean space, Gao, Hug, and Schneider showed in 2003 that in spherical or hyperbolic space, the total measure of totally geodesic…
Remarks on the Rényi Entropy of a sum of IID random variables
Benjamin Jaye, Galyna V. Livshyts, Grigoris Paouris +1
In this note we study a conjecture of Madiman and Wang which predicted that the generalized Gaussian distribution minimizes the Rényi entropy of the sum of independent random varia…
Spherical centroid bodies
Florian Besau, Thomas Hack, Peter Pivovarov +1
The spherical centroid body of a centrally-symmetric convex body in the Euclidean unit sphere is introduced. Two alternative definitions - one geometric, the other probabilistic in…
Affine isoperimetric inequalities on flag manifolds
Susanna Dann, Grigoris Paouris, Peter Pivovarov
Building on work of Furstenberg and Tzkoni, we introduce -flag affine quermassintegrals and their dual versions. These quantities generalize affine and dual affine quermas…