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The Ginibre Ensemble of Real Random Matrices and its Scaling Limits

Borodin, A. and Sinclair, C. D. (2009) The Ginibre Ensemble of Real Random Matrices and its Scaling Limits. Communications in Mathematical Physics, 291 (1). pp. 177-224. ISSN 0010-3616. https://resolver.caltech.edu/CaltechAUTHORS:20090817-144818938

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Abstract

We give a closed form for the correlation functions of ensembles of a class of asymmetric real matrices in terms of the Pfaffian of an antisymmetric matrix formed from a 2 × 2 matrix kernel associated to the ensemble. We apply this result to the real Ginibre ensemble and compute the bulk and edge scaling limits of its correlation functions as the size of the matrices becomes large.


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http://dx.doi.org/10.1007/s00220-009-0874-5DOIArticle
https://rdcu.be/4c5lPublisherFree ReadCube access
https://arxiv.org/abs/0805.2986arXivDiscussion Paper
Additional Information:© 2009 Springer. Received: 27 May 2008 Accepted: 2 April 2009 Published online: 18 July 2009. We thank Percy Deift for helpful early discussions and for introducing the authors to each other. The second author would also like to thank Brian Rider for many helpful discussions regarding the real Ginibre ensemble. We are grateful to Eric Rains for allowing us to include his proof of the Pfaffian Cauchy-Binet formula (Appendix B). We also thank the referee for helpful suggestions and for providing references previously unknown to us. Finally we would like to thank Peter Forrester for keeping us updated about his work. The first named author (A.B.) was partially supported by the NSF grant DMS-0707163.
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Funding AgencyGrant Number
NSFDMS-0707163
Issue or Number:1
Record Number:CaltechAUTHORS:20090817-144818938
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20090817-144818938
Official Citation:Borodin, A. & Sinclair, C.D. Commun. Math. Phys. (2009) 291: 177. https://doi.org/10.1007/s00220-009-0874-5
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:15123
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:08 Sep 2009 16:25
Last Modified:03 Oct 2019 00:55

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