The distribution of Gaussian multiplicative chaos on the unit interval

Rémy, Guillaume; Zhu, Tunan

doi:10.48550/arxiv.1804.02942

Cited by 7 publications

(26 citation statements)

References 22 publications

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“…The BPZ equations are essential for proving integrability of LCFT. They were used in the proof of the DOZZ-formula [14,15] for the 3-point function of LCFT on the sphere, and after this similar methods were used for obtaining integrability results for one dimensional GMC measures on the unit circle [19] and on the unit interval [20]. The unit circle computation was based on a boundary LCFT, which is defined in [11].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Smoothness of Correlation Functions in Liouville Conformal Field Theory

Oikarinen

2019

Ann. Henri Poincaré

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Smoothness of Correlation Functions in Liouville Conformal Field Theory

Oikarinen

2019

Ann. Henri Poincaré

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“…Other results on GMC are also proved in different geometries based on the BPZ equations, such as the Fyodorov Bouchaud's formula [21], the probabilistic distribution of GMC on the unit interval [22] and exact formulas for the boundary Liouville structure constants [11,20] in an upcoming work. All these series of projects prove the BPZ equations of order (2,1) and (1,2) in a different setting and use this to deduce non trivial shift equations of the object in question, which corresponds to the conformal bootstrap method in physics.…”

Section: Introductionmentioning

confidence: 91%

Higher order BPZ equations for Liouville conformal field theory

Zhu

2020

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Inspired by some intrinsic relations between Coulomb gas integrals and Gaussian multiplicative chaos, this article introduces a general mechanism to prove BPZ equations of order (r, 1) and (1, r) in the setting of probabilistic Liouville conformal field theory, a family of conformal field theory which depends on a parameter γ ∈ (0, 2). The method consists in regrouping singularities on the degenerate insertion, and transforming the proof into an algebraic problem. With this method we show that BPZ equations hold on the sphere for the parameter γ ∈ [ √ 2, 2) in the case (r, 1) and for γ ∈ (0, 2) in the case (1, r). The same technique applies to the boundary Liouville field theory when the bulk cosmological constant µ bulk = 0, where we prove BPZ equations of order (r, 1) and (1, r) for γ ∈ (0, 2).

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“…In spite of the importance of the theory, not much is known about the distributional properties of GMC. For instance, given a bounded open set A ⊂ D, one may ask what the exact distribution of M γ (A) is, but nothing is known except in very specific cases where specialised LCFT tools are applicable [28,32,33]. Indeed even the regularity of the distribution (e.g.…”

Section: Introductionmentioning

confidence: 99%

Universal tail profile of Gaussian multiplicative chaos

Wong

2020

Probab. Theory Relat. Fields

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In this article we study the tail probability of the mass of critical Gaussian multiplicative chaos (GMC) associated to a general class of log-correlated Gaussian fields in any dimension, including the Gaussian free field (GFF) in dimension two. More precisely, we derive a fully explicit formula for the leading order asymptotics for the tail probability and demonstrate a new universality phenomenon. Our analysis here shares similar philosophy with the subcritical case but requires a different approach due to complications in the analogous localisation step, and we also employ techniques from recent studies of fusion estimates in GMC theory. 2 γ 2 , d = 1,

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The distribution of Gaussian multiplicative chaos on the unit interval

Cited by 7 publications

References 22 publications

Smoothness of Correlation Functions in Liouville Conformal Field Theory

Smoothness of Correlation Functions in Liouville Conformal Field Theory

Higher order BPZ equations for Liouville conformal field theory

Universal tail profile of Gaussian multiplicative chaos

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