On the Critical–Subcritical Moments of Moments of Random Characteristic Polynomials: A GMC Perspective

We study the ‘critical moments’ of subcritical Gaussian multiplicative chaos (GMCs) in dimensions [Formula: see text] . 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 univ...

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Autores principales: Keating, Jonathan P., Wong, Mo Dick
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9392718/
https://www.ncbi.nlm.nih.gov/pubmed/36003142
http://dx.doi.org/10.1007/s00220-022-04429-3
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author Keating, Jonathan P.
Wong, Mo Dick
author_facet Keating, Jonathan P.
Wong, Mo Dick
author_sort Keating, Jonathan P.
collection PubMed
description We study the ‘critical moments’ of subcritical Gaussian multiplicative chaos (GMCs) in dimensions [Formula: see text] . 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.
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spelling pubmed-93927182022-08-22 On the Critical–Subcritical Moments of Moments of Random Characteristic Polynomials: A GMC Perspective Keating, Jonathan P. Wong, Mo Dick Commun Math Phys Article We study the ‘critical moments’ of subcritical Gaussian multiplicative chaos (GMCs) in dimensions [Formula: see text] . 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. Springer Berlin Heidelberg 2022-06-29 2022 /pmc/articles/PMC9392718/ /pubmed/36003142 http://dx.doi.org/10.1007/s00220-022-04429-3 Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis 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/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Keating, Jonathan P.
Wong, Mo Dick
On the Critical–Subcritical Moments of Moments of Random Characteristic Polynomials: A GMC Perspective
title On the Critical–Subcritical Moments of Moments of Random Characteristic Polynomials: A GMC Perspective
title_full On the Critical–Subcritical Moments of Moments of Random Characteristic Polynomials: A GMC Perspective
title_fullStr On the Critical–Subcritical Moments of Moments of Random Characteristic Polynomials: A GMC Perspective
title_full_unstemmed On the Critical–Subcritical Moments of Moments of Random Characteristic Polynomials: A GMC Perspective
title_short On the Critical–Subcritical Moments of Moments of Random Characteristic Polynomials: A GMC Perspective
title_sort on the critical–subcritical moments of moments of random characteristic polynomials: a gmc perspective
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9392718/
https://www.ncbi.nlm.nih.gov/pubmed/36003142
http://dx.doi.org/10.1007/s00220-022-04429-3
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