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arXiv · 2006.14578

Graph Hörmander Systems

Haojian Li·Marius Junge·Nicholas LaRacuente
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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.

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Haojian Li, Marius Junge, Nicholas LaRacuente. 2020-06-29. Graph Hörmander Systems. https://arxiv.org/abs/2006.14578

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