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Extremal laws for the real Ginibre ensemble. (English) Zbl 1296.60009
Summary: 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 \(n\to \infty\). 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.

MSC:
60B20 Random matrices (probabilistic aspects)
60G25 Prediction theory (aspects of stochastic processes)
60G70 Extreme value theory; extremal stochastic processes
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