Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Logarithmic Sobolev inequalities for infinite dimensional H\"ormander
  type generators on the Heisenberg group   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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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th