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math.MG2022
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…
math.AP2022
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…