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

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

2009-01-13

arxiv.org/abs/0901.1765v6

Journal of Potential Analysis 31, 1 (2009) 79-102

Mathematics

Functional Analysis

26 pages, corrected version, reference added

Scientific paper

10.1007/s11118-009-9126-8

The Heisenberg group is one of the simplest sub-Riemannian settings in which
we can define non-elliptic H\"ormander 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.

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