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Logarithmic Sobolev inequalities for infinite dimensional H\"ormander type generators on the Heisenberg group.

Thu, 08/20/2009 - 23:06 — SomNambul
Authors: James Inglis, Ioannis Papageorgiou
Subjects: Functional Analysis
link: http://arxiv.org/abs/0901.1765
Abstract

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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