Course Material for the past seminar “Random Matrices and Free Probability”
Title: “Random Matrices and Free Probability”
Speaker: Prof. Víctor Pérez Abreu
Centro de Investigación en Matemáticas, A.C (CIMAT), Guanajuato, Mexico
Dates:
Friday, 30th September, 2011
Tuesday, 11th October, 2011
Friday, 14th October, 2011
Time: 10:00 – 11:30 am
Location: Business Campus in Hochbrück, PR 2.01.10, Parkring 13, 85748 Garching
Directions
Abstract:
The eigenvalues of large dimensional random matrices exhibit interesting asymptotic properties. For example, let $X$ be a symmetric $n\times n$ matrix with independent and identically distributed entries with variance 2 on and variance 1 above the diagonal. Then the density of the eigenvalues of $X/\sqrt{n}$ looks like a semicircle for large $n$.
Spectral properties of large random matrices is one of many topics that has become known under the banner Random Matrix Theory (RMT).
Free probability theory is a line of research which parallels aspects of classical probability in a non-commutative context. Therefore it is a natural tool to study random matrices.
This mini-course will give a short introduction to the basic concepts of RMT and Free Probability, and an overview of some of their main results.
Some applications to other areas like wireless communications and statistics will be outlined at the end of the course.
The lecture can be attended without previous notice.
Contact: pfaffel(at)ma.tum.de
- Files:
TUMCourseSep30_final.pdf580 K- TUMCourseOct11Final.pdf567 K
- TUMCourseOct14Final.pdf573 K
- Poster_Seminar_Abreu.pdf657 K
