Random Hermitian matrices and Gaussian multiplicative chaos

Nathanaël Berestycki*, Christian Webb, Mo Dick Wong

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

14 Citations (Scopus)
113 Downloads (Pure)

Abstract

We prove that when suitably normalized, small enough powers of the absolute value of the characteristic polynomial of random Hermitian matrices, drawn from one-cut regular unitary invariant ensembles, converge in law to Gaussian multiplicative chaos measures. We prove this in the so-called (Formula presented.)-phase of multiplicative chaos. Our main tools are asymptotics of Hankel determinants with Fisher–Hartwig singularities. Using Riemann–Hilbert methods, we prove a rather general Fisher–Hartwig formula for one-cut regular unitary invariant ensembles.

Original languageEnglish
Pages (from-to)103-189
Number of pages87
JournalProbability Theory and Related Fields
Volume172
Issue number1-2
Early online date6 Nov 2017
DOIs
Publication statusPublished - Oct 2018
MoE publication typeA1 Journal article-refereed

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