Random Matrices: Theory, Numerical Methods, and Application

What it is about

You will receive an introduction to large random matrices, their eigenvalue distributions and eigenvalue spacings. At the end of the module you will know the fundamental methods (e.g. Stieltjes transform, orthogonal polynomials, Fredholm determinants, free probability) and you will be able to compute limit distributions and apply them to models in applications.

What you will be able to do

• Understand key concepts of large random matrices
• Apply main methods for determining eigenvalue distributions
• Compute limit distributions and spacings
• Use analytical and numerical tools for applications
• Be able to read and use scholarly literature in the field

What the module consists of

• VorlesungPresentation of the content on the electronic board with demonstrative examples and discussion

Teaching method

• Vorlesung auf elektronischer TafelConveying the theory and demonstrative examples
• Diskussion mit StudierendenDeepening understanding and clarification of open questions
• Selbststudium (Aufgaben, Literatur)Complement and deepening of the lecture contents