Dr. Michael Fleermann
I am a Post-Doc in the Stochastics Group of Werner Kirsch. My research focusses on random matrices with correlated entries. The main question I am investigating is how much correlation a random matrix may bear without jeopardizing classical limit results. Thus, I am focussing on
- Semicircle laws under correlations
- Marčenko-Pastur laws under correlations
- Local Laws under correlations
I am also conducting research into the methods of proof needed to obtain the above results, which include
- the method of moments
- the Stieltjes transform method
- random quadratic forms
- High-dimensional sample covariance matrices with Curie-Weiss entries (with Johannes Heiny). Oct. 2019. URL: https://arxiv.org/abs/1910.12332
- The Almost Sure Semicircle Law for Random Band Matrices with Dependent Entries (with Werner Kirsch and Thomas Kriecherbauer). Oct. 2019. URL: https://arxiv.org/abs/1711.10196
- Local Semicircle Law for Curie-Weiss Type Ensembles. Jul. 2019. URL: https://arxiv.org/abs/1907.08782
- Global and Local Semicircle Laws for Random Matrices with Correlated Entries. PhD thesis. FernUniversität in Hagen, Germany, 2019. URL: http://dx.doi.org/10.18445/20190612-122137-0
- Local Laws for Curie-Weiss Random Matrices. August 2019. Summer School in Probability and Mathematical Physics, Ghiffa, Italy.
- Global and Local Semicircle Laws for Random Matrices with Correlated Entries. July 2019. Research Seminar Free Probability, Universität des Saarlandes, Germany.
- Globale und lokale Halbkreisgesetze für Zufallsmatrizen mit korrelierten Einträgen. June 2019. Disputationsvortrag FernUniversität in Hagen, Germany
- Local and Global Limit Laws in Probability and Random Matrix Theory. April 2019. Poster Presentation at conference Random Matrices and Random Graphs, CIRM, France.
- Random Matrices with Curie-Weiss Entries. April 2019. Walkshop KIT 2019, Karlsruhe Institute of Technology, Germany.
- Semicircle Laws for Random Matrices with Curie-Weiss Entries. October 2018. Operations Research Seminar, Universiteit Twente, The Netherlands.
- Semicircle Laws for Random Matrices with Curie-Weiss Entries. September 2018. Summer School in Probability and Mathematical Physics, Ghiffa, Italy.