Multiplicative chaos and the characteristic polynomial of the CUE: The L1-Phase

Miika Nikula*, Eero Saksman, Christian Webb

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)

Abstract

In this article we prove that suitable positive powers of the absolute value of the characteristic polynomial of a Haar distributed random unitary matrix converge in law, as the size of the matrix tends to infinity, to a Gaussian multiplicative chaos measure once correctly normalized. We prove this in the whole L1- or subcritical phase of the chaos measure.

Original languageEnglish
Pages (from-to)3905-3965
Number of pages61
JournalTransactions of the American Mathematical Society
Volume373
Issue number6
DOIs
Publication statusPublished - Jun 2020
MoE publication typeA1 Journal article-refereed

Keywords

  • TOEPLITZ DETERMINANTS
  • RANDOM SURFACES
  • MAXIMUM
  • ASYMPTOTICS
  • EIGENVALUES

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