Obiettivo
Noncommutative probability, also called quantum probability or algebraic
probability theory, is an extension of classical probability theory where the
algebra of random variables is replaced by a possibly noncommutative
algebra. A surprising feature of noncommutative probability is the existence
of many very different notions of independence. The most prominent among them
is freeness or free probability, which was introduced by Voiculescu to study
questions in operator algebra theory. In the last twenty-five years, free
probability has turned into a very active and very competitive research area,
in which analogues for many important probabilistic notions like limit
theorems, infinite divisibility, and L\'evy processes have been discovered. It
also turned out to be closely related to random matrix theory, which has
important applications in quantum physics and telecommunication.
The current project proposes to study the mathematical theory of independence
in noncommutative probability, and the associated convolution products. We
will concentrate on the following topics:
(1) Applications of monotone independence to free probability. Some
applications have been found already, but recent work indicates that much more
is possible.
(2) Analysis of infinitely divisible distributions in classical and free
probability. Common complex analysis methods will be used for both classes,
and we expect more insight into their mutual relations.
(3) Application and development of Lenczewski's matricial free
independence. This concept introduces very new ideas, whose better
understanding will certainly lead to new interesting results.
The methods we will use in this project come not only from noncommutative
probability, but also from functional analysis, complex analysis, combinatorics, classical probability, random matrices, and graph theory.
Campo scientifico
Invito a presentare proposte
FP7-PEOPLE-2012-IIF
Vedi altri progetti per questo bando
Meccanismo di finanziamento
MC-IIF - International Incoming Fellowships (IIF)Coordinatore
25000 Besancon
Francia