Circle-average process of the Gaussian free field
= Circle-average process of the Gaussian free field
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Let $\rho_t$ be uniform measure on the circle of radius $e^{-t}$ around the origin in the unit disc. The process $X_t=(h,\rho_t)$ is the circle-average process. The <Domain Markov property of the Gaussian free field> and the <mean value property for harmonic functions> imply that its increments are independent and stationary.