4 papers
The Gaussian Conjugate Rogers-Shephard Inequality
Emanuel Milman, Shohei Nakamura, Hiroshi Tsuji
We fuse between the Rogers-Shephard inequality for the Lebesgue measure and Royen's Gaussian Correlation Inequality, simultaneously extending both into a single sharp inequality fo…
The Gaussian correlation inequality for centered convex sets and the case of equality
Shohei Nakamura, Hiroshi Tsuji
Inspired by Milman's recent observation, we prove that the Gaussian correlation inequality holds for convex sets having the same barycenter, and especially for centered ones. This…
Duality and Heat flow
Dario Cordero-Erausquin, Nathael Gozlan, Shohei Nakamura +1
We reveal the relation between the Legendre transform of convex functions and heat flow evolution, and how it applies to the functional Blaschke-Santalo inequality. We also describ…
A generalized Legendre duality relation and Gaussian saturation
Shohei Nakamura, Hiroshi Tsuji
Motivated by the barycenter problem in optimal transportation theory, Kolesnikov--Werner recently extended the notion of the Legendre duality relation for two functions to the case…