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.

arXiv comment26 pages, corrected version, reference added

References in corpus (1)

• On gradient bounds for the heat kernel on the Heisenberg group

Cited by in corpus (5)

• Entropy dissipation for degenerate stochastic differential equations via sub-Riemannian density manifold
• A note on the Modified Log-Sobolev inequality
• Concentration inequalities for Gibbs measures
• The log-Sobolev inequality with quadratic interactions
• The log-Sobolev inequality for spin systems of higher order interactions