A log-Sobolev type inequality for free entropy of two projections
arXiv:math/0601171 · doi:10.1214/08-AIHP164
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.
The assumption of the main theorem is improved