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arXiv · 2106.15141

Maxima of log-correlated fields: some recent developments

E. C. Bailey·J. P. Keating
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Abstract

We review recent progress relating to the extreme value statistics of the characteristic polynomials of random matrices associated with the classical compact groups, and of the Riemann zeta-function and other $L$-functions, in the context of the general theory of logarithmically-correlated Gaussian fields. In particular, we focus on developments related to the conjectures of Fyodorov \& Keating concerning the extreme value statistics, moments of moments, connections to Gaussian Multiplicative Chaos, and explicit formulae derived from the theory of symmetric functions.

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E. C. Bailey, J. P. Keating. 2021-06-29. Maxima of log-correlated fields: some recent developments. https://doi.org/10.1088/1751-8121%2Fac4394

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