Published October 2009
| Version Submitted
Journal Article
Open
The Ginibre Ensemble of Real Random Matrices and its Scaling Limits
Creators
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1.
California Institute of Technology
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2.
University of Colorado Colorado Springs
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.
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.Attached Files
Submitted - 0805.2986.pdf
Files
0805.2986.pdf
Additional details
Identifiers
- Eprint ID
- 15123
- Resolver ID
- CaltechAUTHORS:20090817-144818938
Related works
- Describes
- https://arxiv.org/abs/0805.2986 (URL)
Funding
- NSF
- DMS-0707163
Dates
- Created
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2009-09-08Created from EPrint's datestamp field
- Updated
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2021-11-08Created from EPrint's last_modified field