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2018 The maximum deviation of the $\text{Sine} _\beta $ counting process
Diane Holcomb, Elliot Paquette
Electron. Commun. Probab. 23: 1-13 (2018). DOI: 10.1214/18-ECP149

Abstract

In this paper, we consider the maximum of the $\text{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 Prüfer phases of a Gaussian $\beta $–ensemble matrix.

Citation

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Diane Holcomb. Elliot Paquette. "The maximum deviation of the $\text{Sine} _\beta $ counting process." Electron. Commun. Probab. 23 1 - 13, 2018. https://doi.org/10.1214/18-ECP149

Information

Received: 27 January 2018; Accepted: 3 July 2018; Published: 2018
First available in Project Euclid: 12 September 2018

zbMATH: 06964401
MathSciNet: MR3863914
Digital Object Identifier: 10.1214/18-ECP149

Subjects:
Primary: 60B20

JOURNAL ARTICLE
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