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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.

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)
Full Text: DOI Euclid arXiv
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