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Critical Liouville measure as a limit of subcritical measures. (English) Zbl 07055622
Summary: 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.

##### MSC:
 60G15 Gaussian processes 60G60 Random fields 60D05 Geometric probability and stochastic geometry 60G60 Random fields 60K35 Interacting random processes; statistical mechanics type models; percolation theory 60J67 Stochastic (Schramm-)Loewner evolution (SLE)
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