Critical Liouville measure as a limit of subcritical measures

Aru, Juhan; Powell, Ellen; Sepúlveda, Avelio

doi:10.1214/19-ecp209

Critical Liouville measure as a limit of subcritical measures

Aru, Juhan; Powell, Ellen; Sepúlveda, Avelio

Authors

Juhan Aru

Dr Ellen Powell ellen.g.powell@durham.ac.uk
Associate Professor

Avelio Sepúlveda

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