2 citations · 3 across the 11 of their papers we have counts for
11 papers
On the monotonicity of magnitude functions of negative type finite semimetric spaces
Kiyonori Gomi, Hiroshi Tsuji
Motivated by the conjectured monotonicity of the magnitude functions of metric spaces of negative type, we investigate the monotonicity problem for finite semimetric spaces, namely…
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…
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…
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…
The functional volume product under heat flow
Shohei Nakamura, Hiroshi Tsuji
We prove that the functional volume product for even functions is monotone increasing along the Fokker--Planck heat flow. This in particular yields a new proof of the functional Bl…
Analytic aspects of the dilation inequality for symmetric convex sets in Euclidean spaces
Hiroshi Tsuji
We discuss an analytic form of the dilation inequality for symmetric convex sets in Euclidean spaces, which is a counterpart of analytic aspects of Cheeger's isoperimetric inequali…
Hypercontractivity beyond Nelson's time and its applications to Blaschke--Santaló inequality and inverse Santaló inequality
Shohei Nakamura, Hiroshi Tsuji
We explore an interplay between an analysis of diffusion flows such as Ornstein--Uhlenbeck flow and Fokker--Planck flow and inequalities from convex geometry regarding the volume p…
Stability of hypercontractivity, the logarithmic Sobolev inequality, and Talagrand's cost inequality
Neal Bez, Shohei Nakamura, Hiroshi Tsuji
We provide deficit estimates for Nelson's hypercontractivity inequality, the logarithmic Sobolev inequality, and Talagrand's transportation cost inequality under the restriction th…
Dilation type inequalities for strongly-convex sets in weighted Riemannian manifolds
Hiroshi Tsuji
In this paper, we consider a dilation type inequality on a weighted Riemannian manifold, which is classically known as Borell's lemma in high-dimensional convex geometry. We invest…
Symmetrized Talagrand Inequalities on Euclidean Spaces
Hiroshi Tsuji
In this paper, we study the symmetrized Talagrand inequality that was proved by Fathi and has a connection with the Blaschke-Santaló inequality in convex geometry. As corollaries o…