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arXiv · 1802.08433

Critical Liouville measure as a limit of subcritical measures

Juhan Aru·Ellen Powell·Avelio Sepúlveda
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Abstract

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

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Juhan Aru, Ellen Powell, Avelio Sepúlveda. 2019-01-09. Critical Liouville measure as a limit of subcritical measures. https://doi.org/10.1214/19-ecp209

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