The Annals of Applied Probability

Extremal laws for the real Ginibre ensemble

Brian Rider and Christopher D. Sinclair

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Abstract

The real Ginibre ensemble refers to the family of $n\times n$ 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 $n\rightarrow\infty$. 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.

Article information

Source
Ann. Appl. Probab., Volume 24, Number 4 (2014), 1621-1651.

Dates
First available in Project Euclid: 14 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1400073659

Digital Object Identifier
doi:10.1214/13-AAP958

Mathematical Reviews number (MathSciNet)
MR3211006

Zentralblatt MATH identifier
1296.60009

Subjects
Primary: 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52) 60G25: Prediction theory [See also 62M20] 60G70: Extreme value theory; extremal processes

Keywords
Random matrices spectral radius

Citation

Rider, Brian; Sinclair, Christopher D. Extremal laws for the real Ginibre ensemble. Ann. Appl. Probab. 24 (2014), no. 4, 1621--1651. doi:10.1214/13-AAP958. https://projecteuclid.org/euclid.aoap/1400073659


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