Universal tail profile of Gaussian multiplicative chaos

Wong, Mo Dick

doi:10.1007/s00440-020-00960-3

Cited by 8 publications

(11 citation statements)

References 45 publications

(120 reference statements)

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“…The expression (1.11) is reminiscent of the tail expansion of subcritical GMCs, as it was shown in [29] (under extra regularity condition on f ) that…”

Section: Setting and Main Resultsmentioning

confidence: 93%

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

Keating¹,

Wong²

2020

Preprint

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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.

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“…The expression (1.11) is reminiscent of the tail expansion of subcritical GMCs, as it was shown in [29] (under extra regularity condition on f ) that…”

Section: Setting and Main Resultsmentioning

confidence: 93%

“…Despite the connections to large deviation of GMC, our proof is orthogonal to that in [29]. As we shall see later, the analysis here is closely related to the asymptotics for…”

Section: Main Ideamentioning

confidence: 79%

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

Keating¹,

Wong²

2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…The expression ( 12) is reminiscent of the tail expansion of subcritical GMCs, as it was shown in [47] (under extra regularity condition on f ) that…”

Section: Setting and Main Resultmentioning

confidence: 95%

“…On this event, it is actually more convenient to work with the original representation of the integrand, i.e. (47). Since…”

Section: Convergence To the Reflection Coefficientmentioning

confidence: 99%

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

Keating

Wong

2022

Commun. Math. Phys.

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We study the ‘critical moments’ of subcritical Gaussian multiplicative chaos (GMCs) in dimensions $$d \le 2$$ 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.

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“…The parameters µ 1 , µ 2 tune the weights of both sides as we approach the insertion. For more details and results on tail expansions of GMC measures with the reflection coefficients see the works [16,29,31].…”

Section: The Reflection Coefficientmentioning

confidence: 99%

Integrability of boundary Liouville conformal field theory

Rémy¹,

Zhu²

2020

Preprint

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Liouville conformal field theory (LCFT) is considered on a simply connected domain with boundary, specializing to the case where the Liouville potential is integrated only over the boundary of the domain. We work in the probabilistic framework of boundary LCFT introduced by Huang- Rhodes-Vargas (2015). Building upon the known proof of the bulk one-point function by the first author, exact formulas are rigorously derived for the remaining basic correlation functions of the theory, i.e., the bulk-boundary correlator, the boundary two-point and the boundary three-point functions. These four correlations should be seen as the fundamental building blocks of boundary Liouville theory, playing the analogue role of the DOZZ formula in the case of the Riemann sphere. Our study of boundary LCFT also provides the general framework to understand the integrability of one-dimensional Gaussian multiplicative chaos measures as well as their tail expansions. Finally this work sets the stage for studying the more general case of boundary LCFT with both bulk and boundary Liouville potentials.

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Universal tail profile of Gaussian multiplicative chaos

Cited by 8 publications

References 45 publications

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

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

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

Integrability of boundary Liouville conformal field theory

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