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Project A4: Asymptotics of spectral distributions



Summary:

The main focus of this project is the investigation of asymptotic distributions of eigenvalues and eigenvectors of matrices of high dimensional random matrix ensembles as well as spectral distributions of infinite dimensional operators in free probability theory. Another focus is the connection of matrix-valued stochastic processes and their induced spectral processes to representation theory and the limits of related combinatorial structures like Young diagrams and partitions. Furthermore, representation theoretic methods will be used to compute asymptotic approximations to higher correlations of characteristic polynomials. The limiting local and global distributions of eigenvalues appearing in this context are often universal and appear as limiting objects in various contexts of mathematics as well as mathematical physics. A rather incomplete list contains representation theory, asymptotic combinatorics, nuclear growth models in probability, free probability and operator algebras, determinantal point processes, integrable systems as well as the correlations of zeros of L-functions. These similarities ask for an explanation in a more general framework. In this project, we intend to concentrate on some of these connections, connecting probability, algebraic combinatorics and complex analysis. In cooperation with a number of other projects of the CRC we hope to advance the understanding of these surprising connections between different fields.


Links:

Probability Theory and Mathematical Statistics

Recent Preprints:

16049 Friedrich Götze, Alexey Naumov, Alexander Tikhomirov, Dimitry Timushev PDF

On the local semicircular law for Wigner ensembles

Project: A4

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On the local semicircular law for Wigner ensembles


Authors: Friedrich Götze, Alexey Naumov, Alexander Tikhomirov, Dimitry Timushev Projects: A4
Submission Date: 2016-12-23 Submitter: Holger Kösters
Download: PDF Link: 16049

16048 Friedrich Götze, Holger Sambale PDF

Second order concentration via logarithmic Sobolev inequalities

Project: A4

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Second order concentration via logarithmic Sobolev inequalities


Authors: Friedrich Götze, Holger Sambale Projects: A4
Submission Date: 2016-12-23 Submitter: Holger Kösters
Download: PDF Link: 16048

16047 Sergey Bobkov, Gennadiy P. Chistyakov, Friedrich Götze PDF

Rényi divergence and the central limit theorem

Project: A4

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Rényi divergence and the central limit theorem


Authors: Sergey Bobkov, Gennadiy P. Chistyakov, Friedrich Götze Projects: A4
Submission Date: 2016-12-23 Submitter: Holger Kösters
Download: PDF Link: 16047

16045 Mario Kieburg, Holger Kösters PDF

Products of random matrices from polynomial ensembles

Project: A4

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Products of random matrices from polynomial ensembles


Authors: Mario Kieburg, Holger Kösters Projects: A4
Submission Date: 2016-12-23 Submitter: Friedrich Götze
Download: PDF Link: 16045

16044 Mario Kieburg, Holger Kösters PDF

Exact relation between singular value and eigenvalue statistics

Project: A4

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Exact relation between singular value and eigenvalue statistics


Authors: Mario Kieburg, Holger Kösters Projects: A4
Submission Date: 2016-12-23 Submitter: Friedrich Götze
Download: PDF Link: 16044

16006 Zhi Shui Hu, Vladimir Ulyanov, Qun Qiang Feng PDF

Limit theorems for number of edges in the generalized random graphs with random vertex weights

Project: A4

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Limit theorems for number of edges in the generalized random graphs with random vertex weights


Authors: Zhi Shui Hu, Vladimir Ulyanov, Qun Qiang Feng Projects: A4
Submission Date: 2016-02-05 Submitter: Friedrich Götze
Download: PDF Link: 16006

15106 Thomas Kriecherbauer, Martin Venker PDF

Edge Statistics for a Class of Repulsive Particle Systems

Project: A4

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Edge Statistics for a Class of Repulsive Particle Systems


Authors: Thomas Kriecherbauer, Martin Venker Projects: A4
Submission Date: 2015-12-23 Submitter: Friedrich Götze
Download: PDF Link: 15106

15105 Kristina Schubert, Martin Venker PDF

Empirical Spacings of Unfolded Eigenvalues

Project: A4

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Empirical Spacings of Unfolded Eigenvalues


Authors: Kristina Schubert, Martin Venker Projects: A4
Submission Date: 2015-12-23 Submitter: Friedrich Götze
Download: PDF Link: 15105

15104 Holger Kösters, Alexander Tikhomirov PDF

Limiting Spectral Distributions of Sums of Products of non-Hermitian Random Matrices

Project: A4

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Limiting Spectral Distributions of Sums of Products of non-Hermitian Random Matrices


Authors: Holger Kösters, Alexander Tikhomirov Projects: A4
Submission Date: 2015-12-22 Submitter: Friedrich Götze
Download: PDF Link: 15104

15087 Friedrich Götze, Anna Reshetenko PDF

Asymptotic Expansions in Free Limit Theorems

Project: A4

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Asymptotic Expansions in Free Limit Theorems


Authors: Friedrich Götze, Anna Reshetenko Projects: A4
Submission Date: 2015-12-16 Submitter: Michael Röckner
Download: PDF Link: 15087



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