Logarithmic Sobolev inequalities for infinite dimensional Hörmander type generators on the Heisenberg group

Abstract

The Heisenberg group is one of the simplest sub-Riemannian settings in which we can define non-elliptic Hörmander type generators. We can then consider coercive inequalities associated to such generators. We prove that a certain class of nontrivial Gibbs measures with quadratic interaction potential on an infinite product of Heisenberg groups satisfy logarithmic Sobolev inequalities.

26 pages, corrected version, reference added