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    Extremal laws for the real Ginibre ensemble

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    Genre
    Journal Article
    Date
    2014-01-01
    Author
    Rider, B
    Sinclair, CD
    Subject
    Random matrices
    spectral radius
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/5919
    
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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.
    Citation to related work
    Institute of Mathematical Statistics
    Has part
    Annals of Applied Probability
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    ae974a485f413a2113503eed53cd6c53
    http://dx.doi.org/10.34944/dspace/5901
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