Johannes Alt

Graduate Seminar on Probability Theory: Topics in Random Matrix Theory

Summer Term 2025

Lecturer: Prof. Dr. Johannes Alt

 

Random Matrix Theory aims at understanding the behaviour of a typical large matrix. The seminar deals with large random matrices with independent, identically distributed entries. They are the fundamental examples of non-Hermitian random matrices. The celebrated circular law states that their eigenvalues concentrate on a disc in the complex plane when the matrix size tends to infinite. The first goal of the seminar is the proof of this theorem. Then we derive more refined properties of certain class of matrices with iid entries. 

News 

  • The time of the seminar has been changed to Tuesdays 4 pm to 6 pm due to an overlap with the lecture Adv. Topics in Probability Theory by Prof. Ferrari.
  • Preliminary meeting: 28.01.25, 16:15 Uhr, room 2.040.
  • If you can't come to the preliminary meeting please contact Johannes Alt via email.
  • This webpage is still under construction! 

Prerequisites

Measure theory and probability. Some basic knowledge in complex analysis is helpful but not necessary for all talks.  

Time and Place

Tuesdays, 4 pm (ct.) to 6 pm, Seminar room N0.003.  

Files

References 

The first talks will be based on [BC]. Sections 2.6, 2.7 and 2.8 of [T] cover similar materials. Further references will be announced.  

[BC]  C. Bordenave and D. Chafai, Around the circular law, Probab. Surv. 9 (2012), pp. 1–89. Freely available at https://arxiv.org/abs/1109.3343
[T]   T. Tao, Topics in random matrix theory, Graduate Studies in Mathematics, vol. 132, American Mathematical Society, 2012.
  
  

 

 

 

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