Reference number : GC-2017-Q1-01802, amendment number : , agreement type : G, recipient legal name : Nica, Alexandru (University of Waterloo), recipient country : CA, recipient province : nan, recipient city : Ontario, recipient postal code : nan, program name english : Discovery Grants Program - Individual, program name french : Programme de subventions à la découverte - individuelles, program purpose english : The proposal is in the area of free probability theory - a line of research which parallels aspects of classical probability, in a context where tensor products are replaced by free products, and independent random variables are replaced by freely independent noncommutative random variables. Free probability originated in the 1980s, in connection to problems about free products of operator algebras. Since then, it has emerged as a subject in its own right, with connections to other parts of mathematics such as classical probability, algebraic combinatorics, and the theory of random matrices. Through its connection to random matrices, free probability has found applications in quantum information theory and in the area of wireless communications in electrical engineering. 
The objective of the proposed research is to make progress in a direction which is quite active in the present stage of free probability, and concerns the interaction between free independence and other types of independence for random variables (either classical independence, or other types of noncommutative independence). The proposed research also has the feature that it combines in an essential way analytic and combinatorial methods, in the treatment of the problems that are being considered., program purpose french : The proposal is in the area of free probability theory - a line of research which parallels aspects of classical probability, in a context where tensor products are replaced by free products, and independent random variables are replaced by freely independent noncommutative random variables. Free probability originated in the 1980s, in connection to problems about free products of operator algebras. Since then, it has emerged as a subject in its own right, with connections to other parts of mathematics such as classical probability, algebraic combinatorics, and the theory of random matrices. Through its connection to random matrices, free probability has found applications in quantum information theory and in the area of wireless communications in electrical engineering. 
The objective of the proposed research is to make progress in a direction which is quite active in the present stage of free probability, and concerns the interaction between free independence and other types of independence for random variables (either classical independence, or other types of noncommutative independence). The proposed research also has the feature that it combines in an essential way analytic and combinatorial methods, in the treatment of the problems that are being considered., agreement title english : Free probability: combinatorial and analytic aspects, and interactions with other notions of independence, agreement title french : Free probability: combinatorial and analytic aspects, and interactions with other notions of independence, agreement number : RGPIN, agreement value : 100000.0, agreement start date : 2017-05-10, agreement end date : nan, description english : nan, description french : nan, expected results english : nan, expected results french : nan, additional information english : Grant or Award spanning more than one fiscal year. (2017-2018 to 2022-2023), additional information french : Subvention ou bourse octroyée s'appliquant à plus d'un exercice financier. (2017-2018 à 2022-2023), owner organization : nserc-crsng, owner organization title : Natural Sciences and Engineering Research Council of Canada | Conseil de recherches en sciences naturelles et en génie du Canada