Graph Hörmander Systems

Abstract

This paper extends the Bakry-Émery theorem connecting the Ricci curvature and log-Sobolev inequalities to the matrix-valued setting. Using tools from noncommuative geometry, it is shown that for a right invariant second order differential operator on a compact Lie group, a lower bound for a matrix-valued modified log-Sobolev inequality is equivalent to a uniform lower bound for all finite dimensional representations. Using combinatorial tools, we obtain computable lower bounds for matrix-valued log-Sobolev inequalities of graph-Hörmander systems using combinatorial methods.

References in corpus (2)

• Poincaré type inequalities on the discrete cube and in the CAR algebra
• On the Boltzmann Equation for Weakly Nonlinear Wave Equations

Cited by in corpus (1)

• Complete Sobolev Type Inequalities