Community Research and Development Information Service - CORDIS


NCDFP Report Summary

Project ID: 339760
Funded under: FP7-IDEAS-ERC
Country: Germany

Mid-Term Report Summary - NCDFP (Non-Commutative Distributions in Free Probability)

The goal of this project is to study new directions in free probability theory with a high potential to lead to breakthroughs in our understanding of random matrix models and operator algebras. We are driving forward the study of "free analysis'' which is intended to provide a whole new mathematical theory for variables with the highest degree of non-commutativity. We have already made substantial progress in this program. We found and classified new classes of non-commutative symmetries (including, in particular, also symmetries which describe a mixture of commutative and non-commutative situations). We provided effective algorithms to calculate the distribution of large classes of functions in non-commuting variables, yielding also in particular such calculation algorithms for the asymptotic eigenvalue distribution for general random matrix models. (Being able to perform such calculations is of great interest in applied problems, like in the modeling of wireless communication networks). Furthermore, we were able to prove general qualitative properties of such distributions.

Reported by

Follow us on: RSS Facebook Twitter YouTube Managed by the EU Publications Office Top