Free probability theory (Q2577094)

Summary: Free probability theory is a line of research which parallels aspects of classical probability, in a non-commutative context where tensor products are replaced by free products, and independent random variables are replaced by free random variables. The theory grew out of attempts to solve some longstanding problems about von Neumann algebras of free groups. In the almost twenty years since its creation, free probability has become a subject in its own right, with connections to several other parts of mathematics: operator algebras, the theory of random matrices, classical probability and the theory of large deviations, algebraic combinatorics, topology. Free probability also has connections with applied mathematics (wireless communication) and some mathematical models in theoretical physics. The Oberwolfach workshop on free probability brought together a very strong group of mathematicians representing the current directions of development in the area. Contributions: --Ken Dykema, Multilinear Function Series and Transforms in Free Probability Theory p.831 --Teodor Banica (joint with Julien Bichon), Quantum Permutation Groups and Free Probability p.833 --James Mingo (joint with Timothy Kusalik, Roland Speicher), Orthogonal Polynomials and Fluctuations of Random Matrices p.835 --Alice Guionnet, Combinatorial Aspects of Matrix Models p.837 --Florent Benaych-Georges, Rectangular Random Matrices, Freeness with Amalgamation, and Free Entropy p.838 --Dimitri Shlyakhtenko, Applications of \(L^2\) Cohomology to Free Entropy Dimension p.839 --Kenley Jung (joint with Ken Dykema, Dimitri Shlyakhtenko), The Microstates Free Entropy Dimension of a DT-Operator is 2. p.842 --Nathaniel Brown, Finite Free Entropy and Free Group Factors p.842 --Benoit Collins, Integration on Compact Groups and Applications p.844 --Raj Rao (joint with Alan Edelman), The Polynomial Method: From Theory to a Free Calculator p.846 --Alan Edelman (joint with N. Raj Rao, Plamen Koev), Finite Free Cumulants and Moments of Unitary/Orthogonal Matrices .p847 --Franz Lehner, A Free Analogue of Brillinger's Formula p.848 --Uke Haagerup (joint with Hanne Schultz), Invariant Subspaces for Operators in a General II\(_1\)-Factor p.849 --Marek Bozejko (joint with Wlotek Bryc), Free Levy Processes p.850 --Hanne Schultz (joint with Uke Haagerup), Brown Measures of Sets of Commuting Operators in a II\(_1\) Factor p.850 --Michael Anshelevich (joint with Edward G. Ekros, Mihai Popa), Interval Partitions, Hopf Algebras, and the Inversion of Power Series p.850 --Thomas Schick, Introduction to \(L^2\)-Betti Numbers and Their Relation to Free Probability . 852 --Hans Maassen (joint with Muadualin Gutxua), Combinatorial Fock Spaces and Non-Commutative Gaussian Processes p.855 --Palle Jorgensen (joint with Daniil P. Proskurin and Yuriĭ\ S. Samoĭlenko), Deformation of \(C^*\)-algebras on Generators and Relations p.856 --Yoshimichi Ueda (joint with Fumio Hiai), Free Talagrand Inequality p.857 --Mylene Maida (joint with Alice Guionnet) p.861 --Friedrich Götze (joint with Gennadii Chistyakov), Analysis and Arithmetic of Free Convolutions p.864 --Akihito Hora, The limit shape of Young diagrams for Weyl groups of type B p.867 --Piotr Sniady, Gaussian Fluctuations of Yound Diagrams: Connection to Random Matrices p.869 --Mireille Capitaine (joint with M. Casalis), Cumulants for Random Matrices as Convolutions on the Symmetric Group p.872 --Steen Thorbjornsen (joint with Ole Barndorff-Nielsen), Monomorphisms of the Class of Inlnitely Divisible Laws p.874