 Finite-Green-energy measure pairing with a Gaussian free field

ID: finite-green-energy-measure-pairing-with-a-gaussian-free-field

ρ

has finite Green energy, then

(h, ρ) = \sum_{n \geq 1} ξ_{n} \int_{D} e_{n} d ρ

converges in

L^{2}

(e_{n})

H_{0}^{1} (D)

and independent standard normal coefficients

ξ_{n}

. The limit is centered Gaussian with variance equal to the Green energy of

ρ

and does not depend on the chosen basis.

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