Theorie der Zufallsmatrizen

What it is about

You learn non-asymptotic deviation estimates for random variables and vectors (in particular subgaussian and subexponential as well as isotropic vectors) and apply these concepts to random matrices with independent rows or columns. In the end you can formulate statements about the extreme singular values of such matrices, compare them and apply them to concrete examples as well as applications such as dimensionality reduction and Compressed Sensing.

What you will be able to do

• Name and compare singular value estimates for random matrices
• Carry out applications to examples such as dimensionality reduction and Compressed Sensing
• Master essential proof techniques (e.g., union bounds, concentration inequalities)
• Transfer methods to related problems

What the module consists of

• Vorlesungweekly Blackboard lectures convey the theory and proof techniques
• Übungsblätterevery two weeks for deepening; independent solution of the problems
• Recitation/Übungspräsentationbiweekly: students write solutions and present them in the practice format

Teaching method

• Vorlesungintroduces concepts and proof methods
• Self-study of problem sheetssolidifies proving longer results that are not required in the exam
• Presentation in the exercise seminarallows demonstration of developed solutions and promotes understanding/communication