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.
A note on the maximum of the Riemann zeta function, and log-correlated random variables
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
In recent work, Fyodorov and Keating conjectured the maximum size of $|\zeta(1/2+it)|$ in a typical interval of length O(1) on the critical line. They did this by modelling the zeta function by the characteristic polynomial of a random matrix; relating the random matrix problem to another problem from statistical mechanics; and applying a heuristic analysis of that problem. In this note we recover a conjecture like that of Fyodorov and Keating, but using a different model for $|\zeta(1/2+it)|$ in terms of a random Euler product. In this case the probabilistic model reduces to studying the supremum of Gaussian random variables with logarithmic correlations, and can be analysed rigorously.
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UNVERDICTED 2representative citing papers
In a random model of the Riemann zeta function, the normalized total mass of high points a linear order below the maximum converges almost surely to Gaussian multiplicative chaos of an approximating process times a random function.
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High points of a random model of the Riemann-zeta function and Gaussian multiplicative chaos
In a random model of the Riemann zeta function, the normalized total mass of high points a linear order below the maximum converges almost surely to Gaussian multiplicative chaos of an approximating process times a random function.