Complete Logarithmic Sobolev Inequalities via Ricci Curvature Bounded Below II

Understand

Using a non-negative curvature condition, we prove the complete version of modified log-Sobolev inequalities for central Markov semigroups on various compact quantum groups, including group von Neumann algebras, free orthogonal group and quantum automorphism groups.

• We also prove that the "geometric Ricci curvature lower bound" introduced by Junge-Li-LaRacuente is stable under tensor products and amalgamated free products.
• As an application, we obtain the geometric Ricci curvature lower bound and complete modified logarithmic Sobolev inequality for word-length semigroups on free group factors and amalgamated free product algebras.