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Given a planar continuum Gaussian free field $h^{\mathcal U}$ in a domain $\mathcal U$ with Dirichlet boundary condition and any $\delta>0$, we let $\{h_\delta^{\mathcal U}(v): v\in \mathcal U\}$ be a real-valued smooth Gaussian process where $h_\delta^{\mathcal U}(v)$ is the average of $h^{\mathcal U}$ along a circle of radius $\delta$ with center $v$.
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