Random Hermitian matrices and Gaussian multiplicative chaos
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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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en
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87
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Probability Theory and Related Fields, Volume 172, issue 1-2, pp. 103-189
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.Description
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Berestycki, N, Webb, C & Wong, M D 2018, 'Random Hermitian matrices and Gaussian multiplicative chaos', Probability Theory and Related Fields, vol. 172, no. 1-2, pp. 103-189. https://doi.org/10.1007/s00440-017-0806-9