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Logarithmic Sobolev inequalities for infinite dimensional Hörmander type generators on the Heisenberg group. (English) Zbl 1180.22012

Authors’ 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.

MSC:

22E30 Analysis on real and complex Lie groups
39B62 Functional inequalities, including subadditivity, convexity, etc.
60K35 Interacting random processes; statistical mechanics type models; percolation theory
60E15 Inequalities; stochastic orderings
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
58J65 Diffusion processes and stochastic analysis on manifolds
26D10 Inequalities involving derivatives and differential and integral operators
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