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2019 Critical Liouville measure as a limit of subcritical measures
Juhan Aru, Ellen Powell, Avelio Sepúlveda
Electron. Commun. Probab. 24: 1-16 (2019). DOI: 10.1214/19-ECP209

Abstract

We study how the Gaussian multiplicative chaos (GMC) measures $\mu ^\gamma $ corresponding to the 2D Gaussian free field change when $\gamma $ approaches the critical parameter $2$. In particular, we show that as $\gamma \to 2^{-}$, $(2-\gamma )^{-1}\mu ^\gamma $ converges in probability to $2\mu '$, where $\mu '$ is the critical GMC measure.

Citation

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Juhan Aru. Ellen Powell. Avelio Sepúlveda. "Critical Liouville measure as a limit of subcritical measures." Electron. Commun. Probab. 24 1 - 16, 2019. https://doi.org/10.1214/19-ECP209

Information

Received: 9 March 2018; Accepted: 5 January 2019; Published: 2019
First available in Project Euclid: 23 March 2019

zbMATH: 07055622
MathSciNet: MR3933042
Digital Object Identifier: 10.1214/19-ECP209

Subjects:
Primary: 60D05, 60G15, 60G60
Secondary: 60G60, 60J67, 60K35

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