Mathematics – Operator Algebras
Scientific paper
2003-10-29
Mathematics
Operator Algebras
Scientific paper
Biane proved the free analog of the logarithmic Sobolev inequality for probability measures on the real line by means of random matrix approximation procedure. We show that the same method can be applied to reprove Biane and Voiculescu's free analog of Talagrand's transportation cost inequality for measures on the real line. Furthermore, we prove the free analogs of the logarithmic Sobolev inequality and the transportation cost inequality for measures on 1-dimensional torus as well by extending the method to special unitary random matrices.
Hiai Fumio
Petz Denes
Ueda Yoshimichi
No associations
LandOfFree
Inequalities related to free entropy derived from random matrix approximation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Inequalities related to free entropy derived from random matrix approximation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Inequalities related to free entropy derived from random matrix approximation will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-199845