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math.PR2022
Proof Methods in Random Matrix Theory
Michael Fleermann, Werner Kirsch
In this survey article, we give an introduction to two methods of proof in random matrix theory: The method of moments and the Stieltjes transform method. We thoroughly develop the…
math.PR2022
The Central Limit Theorem for Weakly Dependent Random Variables by the Moment Method
Michael Fleermann, Werner Kirsch
In this paper, we derive a central limit theorem for collections of weakly correlated random variables indexed by discrete metric spaces, where the correlation decays in the distan…
math.PR2022★ 3 cited
Random Band and Block Matrices with Correlated Entries
Riccardo Catalano, Michael Fleermann, Werner Kirsch
In this paper, we derive limit laws for the empirical spectral distributions of random band and block matrices with correlated entries. In the first part of the paper, we study ban…