Proves scale-invariant boundary Harnack principle on uniform domains under scale-invariant elliptic Harnack inequality without geodesic assumption or a priori Green functions.
Dirichlet Forms and Symmetric Markov Processes
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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.
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Boundary Harnack principle on uniform domains
Proves scale-invariant boundary Harnack principle on uniform domains under scale-invariant elliptic Harnack inequality without geodesic assumption or a priori Green functions.
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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.