Graph Hörmander Systems
Abstract
This paper extends the Bakry-Émery theorem connecting the Ricci curvature and log-Sobolev inequalities to the matrix-valued setting. Using tools from noncommuative geometry, it is shown that for a right invariant second order differential operator on a compact Lie group, a lower bound for a matrix-valued modified log-Sobolev inequality is equivalent to a uniform lower bound for all finite dimensional representations. Using combinatorial tools, we obtain computable lower bounds for matrix-valued log-Sobolev inequalities of graph-Hörmander systems using combinatorial methods.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2020
- DOI:
- 10.48550/arXiv.2006.14578
- arXiv:
- arXiv:2006.14578
- Bibcode:
- 2020arXiv200614578L
- Keywords:
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- Mathematical Physics;
- Mathematics - Differential Geometry;
- Mathematics - Functional Analysis