A random set is local for a Gaussian free field if, conditionally on the set and its associated harmonic function, the remaining field is an independent zero-boundary field in its complement. This extends the deterministic Domain Markov property of the Gaussian free field to appropriate random revealed domains. Arbitrary field-dependent random sets need not have this property.

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  1. Domain Markov property of the Gaussian free field
  2. Zero-boundary Gaussian free field
  3. Continuum Gaussian free field
  4. Gaussian free field
  5. Gaussian random field
  6. Gaussian process
  7. Stochastic process
  8. Probability theory
  9. Probability and statistics
  10. Area of mathematics
  11. Mathematics
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