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In Liouville quantum gravity (or $2d$-Gaussian multiplicative chaos) one seeks to define a measure $\mu^h = e^{\gamma h(z)} dz$ where $h$ is an instance of the Gaussian free field on a planar domain $D$.
Propriétés locales des fonctions à séries de Fourier aléatoires
J.-P. Kahane · 1960
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A general class of quantum fields without cut-offs in two space-time dimensions
Raphael Høegh-Krohn · 1971
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Possible refinement of the lognormal hypothesis concerning the distribution of energy dissipation in intermittent turbulence
Benoit B Mandelbrot · 1972
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Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier
Benoit B. Mandelbrot · 1974
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The Brunn-Minkowski inequality in Gauss space
Christer Borell · 1975
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Norms of gaussian sample functions
BS Cirel’soN, IA Ibragimov, and VN Sudakov · 1976
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Sur le chaos multiplicatif
Jean-Pierre Kahane · 1985
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Some applications of covariance identities and inequalities to functions of multivariate normal variables
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Equivalence of Liouville measure and Gaussian free field
Nathanaël Berestycki, Scott Sheffield, and Xin Sun · 2014
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Gaussian multiplicative chaos and applications: a review
Rémi Rhodes and Vincent Vargas · 2014
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An elementary approach to Gaussian multiplicative chaos
Nathanaël Berestycki · 2015
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The uniqueness of the Gaussian multiplicative chaos revisited
Janne Junnila and Eero Saksman · 2015
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Bertrand Duplantier and Scott Sheffield · 2011
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