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Limit Theorems for Random Matrices

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Limit Theorems in Probability, Statistics and Number Theory

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 42))

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Abstract

This note gives a survey of some results on limit theorems for random matrices that have been obtained during the last 10 years in the joint research of the author and F. Götze. We consider the rate of convergence to the semi-circle law and Marchenko–Pastur law, Stein’s method for random matrices, the proof of the circular law, and some limit theorems for powers and products of random matrices.

2010 Mathematics Subject Classification. 60F05.

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Acknowledgements

Alexander Tikhomirov partially was supported by SFB 701, by grants of RFBR N 11-01-00310-a, N 11-01-122104-ofi-m-2011, and by Program of Basic Research of Urals Division of RAS.

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Authors and Affiliations

  1. Department of Mathematics, Komi Research Center Ural Branch of Russian Academy of Sciences, Syktyvkar State University, Chernova 3a, 197001, Syktyvkar, Russia

    Alexander Tikhomirov

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  1. Alexander Tikhomirov
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Editors and Affiliations

  1. Mathematics Faculty, Ruhr-University Bochum, Universitätstr. 150, Bochum, 44780, Germany

    Peter Eichelsbacher

  2. Mathematics Faculty, University of Bielefeld, Universitätsstr. 25, Bielefeld, 33615, Germany

    Guido Elsner

  3. Mathematics Faculty, University of Bielefeld, Universitätsstr. 25, Bielefeld, 33615, Germany

    Holger Kösters

  4. Institute for Mathematical Statistics, University of Münster, Einsteinstrasse 62, Münster, 48149, Germany

    Matthias Löwe

  5. Mathematics Institute, University of München, Theresienstr. 39, München, 80333, Germany

    Franz Merkl

  6. Centre for Mathematics, Technische Universität München, Boltzmannstr. 3, Garching bei München, 85747, Germany

    Silke Rolles

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Dedicated to Friedrich Götze on the occasion of his sixtieth birthday

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Tikhomirov, A. (2013). Limit Theorems for Random Matrices. In: Eichelsbacher, P., Elsner, G., Kösters, H., Löwe, M., Merkl, F., Rolles, S. (eds) Limit Theorems in Probability, Statistics and Number Theory. Springer Proceedings in Mathematics & Statistics, vol 42. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36068-8_14

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