A log-Sobolev type inequality for free entropy of two projections

Details A log-Sobolev type inequality for free entropy of two projections A log-Sobolev type inequality for free entropy of two projections

2006-01-09

arxiv.org/abs/math/0601171v3

Mathematics

Operator Algebras

The assumption of the main theorem is improved

Scientific paper

We prove an inequality between the free entropy and the mutual free Fisher
information for two projections, regarded as a free analog of the logarithmic
Sobolev inequality. The proof is based on the random matrix approximation
procedure via the Grassmannian random matrix model of two projections.

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