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

Fumio Hiai·Yoshimichi Ueda
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Abstract

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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Fumio Hiai, Yoshimichi Ueda. 2006-01-09. A log-Sobolev type inequality for free entropy of two projections. https://doi.org/10.1214/08-aihp164

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