Abstract
Maximization problems are solved for Voiculescu's free entropy of probability measures supported in R, R+, and [-1, 1], respectively, under constraint of the pth moment for any p > 0 and implications of these results for multivariate free entropy are discussed in the setting of noncommutative random variables. Similar extremum problems are treated for probability measures on C and Tunder certain constraints. The elliptic law and a distribution found earlier in quantum physics are encountered. These results are in the setting of potential theory and can be viewed independently from Voiculescu's work. The machinery of weighted potentials is exploited.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
