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Graph H\"ormander Systems
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Graph H\"ormander Systems
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This paper extends the Bakry-\'{E}mery 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-H\"ormander systems using combinatorial methods.
Forward citations
Cited by 1 Pith paper
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Intertwining Properties for Bimodule Quantum Markov Semigroups
The authors investigate intertwining properties for bimodule GNS- and KMS-symmetric quantum Markov semigroups, compare them to Bakry-Émery estimates obtained from quantum Fourier analysis, and supply examples.
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