Non-commutative Distributions(Summer Semester 2019)
- There are handwritten lecture notes online available
LectureMonday and Friday, 12:00 -- 13:30, Lecture Hall IV, Building E2 4
The lectures will present some of the main progress which we made in recent years concerning our investigations of non-commutative distributions of non-commuting operators or random matrices. In particular, a basic problem is to find a good approach to the meaning of “non-commutative distribution”. In particular, the lectures will cover:
For more details and updates see the blog of Roland Speicher.
Lecture notesThe lectures will be recorded and the videos will be uploaded on our video platform.
TutorialsDate & Time: Mon 14-16
Room: 8 (318)
Tutor Alexander Mang (alex.mang[at]t-online.de).
ProblemsExercise Sheet 1
Exercise Sheet 2
Exercise Sheet 3
Exercise Sheet 4
Exercise Sheet 5
Exercise Sheet 6
Exercise Sheet 7
Exercise Sheet 8
Exercise Sheet 9
- L.A. Harris: Fixed Points of Holomorphic Mappings for Domains in Banach Spaces. Abstract and Applied Analysis, 2003 link
- D. Jekel. Operator-Valued Non-Commutative Probability link
- Kaliuzhnyi-Verbovetskyi, Dmitry S., and Victor Vinnikov. Foundations of free noncommutative function theory. Mathematical Surveys and Monographs, Vol. 199. American Mathematical Soc., 2014.
- S. Krantz: The Caratheodory and Kobayashi Metrics and Applications in Complex Analysis. The American Mathematical Monthly, 2008 link
James A. Mingo, Roland Speicher: Free Probability and Random Matrices.
Fields Institute Monographs, Vol. 35, Springer, New York, 2017.
Roland Speicher: Free Probability Theory; and its Avatars in Representation Theory,
Random Matrices, and Operator Algebras; also Featuring: Non-commutative Distributions.
Jahresber. Dtsch. Math. Ver. (2017) 119: 3.
- Speicher, Roland. Combinatorial theory of the free product with amalgamation and operator-valued free probability theory. Vol. 627. Memoir of American Mathematical Soc., 1998. link
updated: 7 June 2019 Tobias Mai