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    Overcrowding asymptotics for the Sine(beta) process

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    euclid.aihp.1500624035.pdf
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    Author
    Holcomb, Diane
    Valkó, Benedek
    Affiliation
    Univ Arizona, Dept Math
    Issue Date
    2017-08
    Keywords
    beta-ensembles
    Random matrices
    Overcrowding
    
    Metadata
    Show full item record
    Publisher
    INST MATHEMATICAL STATISTICS
    Citation
    Overcrowding asymptotics for the Sine(beta) process 2017, 53 (3):1181 Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
    Journal
    Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
    Rights
    © Association des Publications de l’Institut Henri Poincaré, 2017.
    Collection Information
    This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.
    Abstract
    We give overcrowding estimates for the Sine(beta) process, the bulk point process limit of the Gaussian beta-ensemble. We show that the probability of having exactly n points in a fixed interval is given by e(-beta/2n2) log(n)+O(n(2)) as n -> infinity. We also identify the next order term in the exponent if the size of the interval goes to zero.
    ISSN
    0246-0203
    DOI
    10.1214/16-AIHP752
    Version
    Final published version
    Sponsors
    National Science Foundation CAREER award [DMS-1053280]
    Additional Links
    http://projecteuclid.org/euclid.aihp/1500624035
    ae974a485f413a2113503eed53cd6c53
    10.1214/16-AIHP752
    Scopus Count
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    UA Faculty Publications

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