Convergence to equilibrium for hypoelliptic non-symmetric Ornstein-Uhlenbeck type operators

Abstract

We study a generalized curvature dimension inequality which is suitable for subelliptic Ornstein-Uhlenbeck type operators and deduce convergence to equilibrium in the $L^2$ and entropic sense. The main difficulty is that the operators we consider may not be symmetric. Our results apply in particular to Ornstein-Uhlenbeck operators on two-step Carnot groups.