Translator Disclaimer
2015 The characteristic polynomial of a random unitary matrix and Gaussian multiplicative chaos - The $L^2$-phase
Christian Webb
Author Affiliations +
Electron. J. Probab. 20: 1-21 (2015). DOI: 10.1214/EJP.v20-4296

Abstract

We study the characteristic polynomial of Haar distributed random unitary matrices. We show that after a suitable normalization, as one increases the size of the matrix, powers of the absolute value of the characteristic polynomial as well as powers of the exponential of its argument converge in law to a Gaussian multiplicative chaos measure for small enough real powers. This establishes a connection between random matrix theory and the theory of Gaussian multiplicative chaos.

Citation

Download Citation

Christian Webb. "The characteristic polynomial of a random unitary matrix and Gaussian multiplicative chaos - The $L^2$-phase." Electron. J. Probab. 20 1 - 21, 2015. https://doi.org/10.1214/EJP.v20-4296

Information

Accepted: 6 October 2015; Published: 2015
First available in Project Euclid: 4 June 2016

zbMATH: 1328.15052
MathSciNet: MR3407221
Digital Object Identifier: 10.1214/EJP.v20-4296

Subjects:
Primary: 15A52
Secondary: 60G57

JOURNAL ARTICLE
21 PAGES


SHARE
Vol.20 • 2015
Back to Top