Open Access
2014 Gaussian multiplicative chaos and applications: A review
Rémi Rhodes, Vincent Vargas
Probab. Surveys 11: 315-392 (2014). DOI: 10.1214/13-PS218


In this article, we review the theory of Gaussian multiplicative chaos initially introduced by Kahane’s seminal work in 1985. Though this beautiful paper faded from memory until recently, it already contains ideas and results that are nowadays under active investigation, like the construction of the Liouville measure in $2d$-Liouville quantum gravity or thick points of the Gaussian Free Field. Also, we mention important extensions and generalizations of this theory that have emerged ever since and discuss a whole family of applications, ranging from finance, through the Kolmogorov-Obukhov model of turbulence to $2d$-Liouville quantum gravity. This review also includes new results like the convergence of discretized Liouville measures on isoradial graphs (thus including the triangle and square lattices) towards the continuous Liouville measures (in the subcritical and critical case) or multifractal analysis of the measures in all dimensions.


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Rémi Rhodes. Vincent Vargas. "Gaussian multiplicative chaos and applications: A review." Probab. Surveys 11 315 - 392, 2014.


Published: 2014
First available in Project Euclid: 3 November 2014

zbMATH: 1316.60073
MathSciNet: MR3274356
Digital Object Identifier: 10.1214/13-PS218

Primary: 60G57
Secondary: 60G15, 28A80

Keywords: Gaussian multiplicative chaos , Gaussian process , KPZ , multifractal measures , review

Rights: Copyright © 2014 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.11 • 2014
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