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Critical Liouville measure as a limit of subcritical measures
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math.PRmath-phmath.MP
keywords
gammacriticalgaussianmeasuremeasuresapproacheschangechaos
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.
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