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Extremal laws for the real Ginibre ensemble

Rider, B
; 
Sinclair, CD
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Journal Article
Date
2014-01-01
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Random matrices
 spectral radius
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http://hdl.handle.net/20.500.12613/5919
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euclid.aoap.1400073659.pdf
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DOI
10.1214/13-AAP958
Abstract
The real Ginibre ensemble refers to the family of n~n matrices in which each entry is an independent Gaussian random variable of mean zero and variance one. Our main result is that the appropriately scaled spectral radius converges in law to a Gumbel distribution as n → ∞. This fact has been known to hold in the complex and quaternion analogues of the ensemble for some time, with simpler proofs. Along the way we establish a new form for the limit law of the largest real eigenvalue. © 2014 Institute of Mathematical Statistics.
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Institute of Mathematical Statistics
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Annals of Applied Probability
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