Random Hermitian matrices and Gaussian multiplicative chaos

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  • University of Cambridge

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.

Details

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

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