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The extremal landscape for the C$\beta$E ensemble

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arxiv 2209.06743 v3 pith:5G56VOSD submitted 2022-09-14 math.PR

Elliot Paquette , Ofer Zeitouni This is my paper · ORCID
classification math.PR
keywords betaensemblelandscapevariableanothercenteredcharacteristiccharacterize
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abstract

We consider the extremes of the logarithm of the characteristic polynomial of matrices from the C$\beta$E ensemble. We prove convergence in distribution of the centered maxima (of the real and imaginary parts) towards the sum of a Gumbel variable and another independent variable, which we characterize as the total mass of a "derivative martingale". We also provide a description of the landscape near extrema points.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On the $\beta=2$ Partition function for Dirichlet $L$-functions in the $q$-aspect

    math.NT 2026-08 conditional novelty 7.0 of 10

    Upper bounds for the q-aspect beta=2 partition function of Dirichlet L-functions and for the typical maximum, matching FHK predictions to second order.

  2. Black Holes and Random Variables

    hep-th 2026-07 unverdicted novelty 6.0 of 10

    High-energy CFT and black-hole interval counts are conjectured to obey the FHK extreme-value law; the resulting O(1) erratic fluctuations limit semiclassical AdS precision to e^{-S0}.

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