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Gaussian free fields for mathematicians by Scott Sheffield (2006)

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By Scott Sheffield.
arxiv.org/abs/math/0312099
arXiv math/0312099v3, 23 November 2006. Section 2: Hilbert/Dirichlet-space and basis constructions; Section 2.8: circle averages. The wiki explicitly chooses its own 1/(2pi) energy normalization and associated logarithmic Green kernel.

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  • Circle-average process of the Gaussian free field
  • Finite-Green-energy measure pairing with a Gaussian free field
  • Green-kernel expansion in the Dirichlet space

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