Discrete logarithmic Sobolev inequalities in Banach spaces

Dario Cordero-Erausquin, Alexandros Eskenazis

Let ${\mathcal{C}}_n=\{-1,1{\}}^n$ be the discrete hypercube equipped with the uniform probability measure ${\sigma }_n$. We prove that if $(E,\Vert \cdot {\Vert }_E)$ is a Banach space of finite cotype…