The paper establishes entropic repulsion of the norm and freezing of angular components in conditioned vector-valued Gaussian free fields, plus bounded norms and phase transitions for massive scalar cases.
Quantitative bounds on vortex fluctuations in 2d Coulomb gas and maximum of the integer-valued Gaussian free field
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Vector-valued Gaussian free field conditioned to avoid a ball: Entropic repulsion of the norm and Freezing of spins
The paper establishes entropic repulsion of the norm and freezing of angular components in conditioned vector-valued Gaussian free fields, plus bounded norms and phase transitions for massive scalar cases.