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

Keating, Jonathan P.; Wong, Mo Dick

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


Authors

Jonathan P. Keating



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.

Citation

Keating, J. P., & Wong, M. D. (2022). On the critical-subcritical moments of moments of random characteristic polynomials: a GMC perspective. Communications in Mathematical Physics, 394(3), 1247-1301. https://doi.org/10.1007/s00220-022-04429-3

Journal Article Type Article
Acceptance Date May 20, 2022
Online Publication Date Jun 29, 2022
Publication Date 2022-09
Deposit Date May 31, 2022
Publicly Available Date Feb 1, 2023
Journal Communications in Mathematical Physics
Print ISSN 0010-3616
Electronic ISSN 1432-0916
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 394
Issue 3
Pages 1247-1301
DOI https://doi.org/10.1007/s00220-022-04429-3
Public URL https://durham-repository.worktribe.com/output/1203808
Related Public URLs https://arxiv.org/abs/2012.15851

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Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/

Copyright 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/.





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