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On the critical-subcritical moments of moments of random characteristic polynomials: a GMC perspective

Keating, Jonathan P. and Wong, Mo Dick (2022) 'On the critical-subcritical moments of moments of random characteristic polynomials: a GMC perspective.', Communications in Mathematical Physics .

Abstract

We study the ‘critical moments’ of subcritical Gaussian multiplicative chaos (GMCs) in dimensions d≤2. In particular, we establish a fully explicit formula for the leading order asymptotics, which is closely related to large deviation results for GMCs and demonstrates a similar universality feature. We conjecture that our result correctly describes the behaviour of analogous moments of moments of random matrices, or more generally structures which are asymptotically Gaussian and log-correlated in the entire mesoscopic scale. This is verified for an integer case in the setting of circular unitary ensemble, extending and strengthening the results of Claeys et al. and Fahs to higher-order moments.

Item Type:Article
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1007/s00220-022-04429-3
Publisher statement:This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Date accepted:20 May 2022
Date deposited:01 June 2022
Date of first online publication:29 June 2022
Date first made open access:27 July 2022

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