Critical Liouville measure as a limit of subcritical measures

Aru, Juhan; Powell, Ellen; Sepúlveda, Avelio

Abstract

We study how the Gaussian multiplicative chaos (GMC) measures μγ corresponding to the 2D Gaussian free field change when γ approaches the critical parameter 2. In particular, we show that as γ→2−, (2−γ)−1μγ converges in probability to 2μ′, where μ′ is the critical GMC measure.

Citation

Aru, J., Powell, E., & Sepúlveda, A. (2019). Critical Liouville measure as a limit of subcritical measures. Electronic Communications in Probability, 24, 1-16. https://doi.org/10.1214/19-ecp209

• Journal Article Type: Article
• Acceptance Date: Jan 5, 2019
• Online Publication Date: Mar 23, 2019
• Publication Date: Mar 23, 2019
• Deposit Date: Sep 28, 2019
• Publicly Available Date: Oct 7, 2019
• Journal: Electronic Communications in Probability
• Publisher: Bernoulli Society for Mathematical Statistics and Probability
• Peer Reviewed: Peer Reviewed
• Volume: 24
• Article Number: 18
• Pages: 1-16
• DOI: https://doi.org/10.1214/19-ecp209