Non-Commutative Stochastic Independence: Algebraic and Analytic Aspects

• Applicants: Dr. Malte Gerhold; Professor Dr. Michael Schürmann
• Subject Area: Mathematics
• Term: from 2018 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 397960675

The aim of the project is to discuss the role of independence in non-commutative probability theory and to investigate the closely related concept of Lévy processes. There are two main directions: On the one hand, we wish to develop a unified treatment of large classes of notions of non-commutative independence which are studied now or will be studied in the future. Questions concerning the classification of notions of non-commutative independence under different sets of axioms also belong to this line of research. On the other hand, we aim at a good understanding of the most common notion of non-commutative independence, the tensor independence, which corresponds to independence of observables in quantum mechanics; specifically, we want to solve the problem of classifying the finitely generated product systems, study Lévy processes on braided Hopf algebras, and get more explicit descriptions of the generators of Lévy processes on compact quantum groups.

• DFG Programme: Research Grants
• International Connection: France, Japan
• Cooperation Partners: Professor Dr. Uwe Franz; Professor Dr. Takahiro Hasebe; Dr. Michael Ulrich