Formulates an avatar of the Fyodorov-Hiary-Keating conjecture for black hole microstate counts, implying sharp bounds on CFT primary operator interval counts and suggesting that AdS spectra exhibit extreme value statistics of Gaussian log-correlated random matrices.
The characteristic polynomial of a random unitary matrix and Gaussian multiplicative chaos - The $L^2$-phase
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abstract
We study the characteristic polynomial of Haar distributed random unitary matrices. We show that after a suitable normalization, as one increases the size of the matrix, powers of the absolute value of the characteristic polynomial as well as powers of the exponential of its argument converge in law to a Gaussian multiplicative chaos measure for small enough real powers. This establishes a connection between random matrix theory and the theory of Gaussian multiplicative chaos.
fields
hep-th 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Black Holes and Random Variables
Formulates an avatar of the Fyodorov-Hiary-Keating conjecture for black hole microstate counts, implying sharp bounds on CFT primary operator interval counts and suggesting that AdS spectra exhibit extreme value statistics of Gaussian log-correlated random matrices.