Extremal laws for the real Ginibre ensemble

DOI10.1214/13-AAP958zbMATH Open1296.60009arXiv1209.6085OpenAlexW3105524422MaRDI QIDQ2511560

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Publication date: 6 August 2014

Published in: (Search for Journal in Brave)

Abstract: The real Ginibre ensemble refers to the family of $nimesn$ 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 $nightarrowinfty$. 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.

Full work available at URL: https://arxiv.org/abs/1209.6085

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