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arXiv · 1701.03289

Random Hermitian Matrices and Gaussian Multiplicative Chaos

Nathanaël Berestycki·Christian Webb·Mo Dick Wong
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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 $L^2$-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.

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Nathanaël Berestycki, Christian Webb, Mo Dick Wong. 2017-01-12. Random Hermitian Matrices and Gaussian Multiplicative Chaos. https://arxiv.org/abs/1701.03289

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