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INST MATHEMATICAL STATISTICSCitation
Overcrowding asymptotics for the Sine(beta) process 2017, 53 (3):1181 Annales de l'Institut Henri Poincaré, Probabilités et StatistiquesRights
© 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
0246-0203Version
Final published versionSponsors
National Science Foundation CAREER award [DMS-1053280]Additional Links
http://projecteuclid.org/euclid.aihp/1500624035ae974a485f413a2113503eed53cd6c53
10.1214/16-AIHP752