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The maximum deviation of the Sine(beta) counting process
KTH.
Ohio State Univ, Columbus, OH 43210 USA..
2018 (English)In: Electronic Communications in Probability, ISSN 1083-589X, E-ISSN 1083-589X, Vol. 23, article id 58Article in journal (Refereed) Published
Abstract [en]

In this paper, we consider the maximum of the Sine(beta) counting process from its expectation. We show the leading order behavior is consistent with the predictions of log-correlated Gaussian fields, also consistent with work on the imaginary part of the log-characteristic polynomial of random matrices. We do this by a direct analysis of the stochastic sine equation, which gives a description of the continuum limit of the Prufer phases of a Gaussian beta-ensemble matrix.

Place, publisher, year, edition, pages
UNIV WASHINGTON, DEPT MATHEMATICS , 2018. Vol. 23, article id 58
Keywords [en]
random matrices, log-correlated field, characteristic polynomial, point process, diffusion, sine process, Sine-beta, stochastic sine equation, extreme values
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:kth:diva-235612DOI: 10.1214/18-ECP149ISI: 000444727200003Scopus ID: 2-s2.0-85053698076OAI: oai:DiVA.org:kth-235612DiVA, id: diva2:1252145
Note

QC 20181001

Available from: 2018-10-01 Created: 2018-10-01 Last updated: 2018-10-01Bibliographically approved

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