4 papers
A characterization of a class of convex log-Sobolev inequalities on the real line
Yan Shu, Michał Strzelecki
We give a sufficient and necessary condition for a probability measure on the real line to satisfy the logarithmic Sobolev inequality for convex functions. The condition is exp…
Hamilton-Jacobi equations on graph and applications
Yan Shu
This paper introduces a notion of gradient and an infimal-convolution operator that extend properties of solutions of Hamilton Jacobi equations to more general spaces, in particula…
Curvature and transport inequalities for Markov chains in discrete spaces
Max Fathi, Yan Shu
We study various transport-information inequalities under three different notions of Ricci curvature in the discrete setting: the curvature-dimension condition of Bakry and Émery,…
Characterization of a class of weak transport-entropy inequalities on the line
Nathael Gozlan, Cyril Roberto, Paul-Marie Samson +2
We study an optimal weak transport cost related to the notion of convex order between probability measures. On the real line, we show that this weak transport cost is reached for a…