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We consider the discrete Gaussian Free Field (DGFF) in scaled-up (square-lattice) versions of suitably regular continuum domains $D\subset\mathbb C$ and describe the scaling limit, including local structure, of the level sets at heights growing as a $\lambda$-multiple of the height of the absolute maximum, for any $\lambda\in(0,1)$.
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2014
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B. Duplantier, R. Rhodes, S. Sheffield and V. Vargas (2014). Critical Gaussian multiplicative chaos: Convergence of the derivative martingale. Ann. Probab
D. Belius and W. Wu (2016). Maximum of the Ginzburg-Landau fields, arXiv:1610.04195
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M. Biskup and O. Louidor (2016). Extreme local extrema of two-dimensional discrete Gaussian free field. Commun. Math. Phys
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2014
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B. Duplantier, R. Rhodes, S. Sheffield and V. Vargas (2014). Renormalization of critical Gaussian multiplicative chaos and KPZ formula. Commun. Math. Phys
2014
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R. Rhodes and V. Vargas (2014). Gaussian multiplicative chaos and applications: A review. Probab. Surveys
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A. Shamov (2014). On Gaussian multiplicative chaos. arXiv:1407.4418
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2016
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