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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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