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Spacings: An Example for Universality in Random Matrix Theory

  • Thomas Kriecherbauer
  • Kristina Schubert
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 53)

Abstract

Universality of local eigenvalue statistics is one of the most striking phenomena of Random Matrix Theory, that also accounts for a lot of the attention that the field has attracted over the past 15 years. In this paper we focus on the empirical spacing distribution and its Kolmogorov distance from the universal limit. We describe new results, some analytical, some numerical, that are contained in Schubert K (2012) On the convergence of the nearest neighbour eigenvalue spacing distribution for orthogonal and symplectic ensembles. PhD thesis, Ruhr-Universität Bochum, Germany. A large part of the paper is devoted to explain basic definitions and facts of Random Matrix Theory, culminating in a sketch of the proof of a weak version of convergence for the empirical spacing distribution σ N (see (23)).

Notes

Acknowledgements

Both authors acknowledge support from the Deutsche Forschungsgemeinschaft in the framework of the SFB/TR 12 “Symmetries and Universality in Mesoscopic Systems”. We are grateful to Peter Forrester for useful remarks.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.University of BayreuthBayreuthGermany

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