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  "body": "\n## Summary\n\nThe Gaussian free field is a random function whose law is Gaussian, with covariance given by the Green function of the [[Laplacian|0E0B6RA8K0]].\nIn the continuum it is a random generalised function rather than a function.\nIt is the natural Gaussian analogue of a [[harmonic function|0DEB0JMN0W]] with random fluctuations.\nIn two dimensions the continuum field is conformally invariant and log-correlated.\nIt appears in statistical physics, in random surfaces and in the theory of the Schramm–Loewner evolution.\n\n## Explanations\n\n### L1 human\n\nThink of a random landscape over a grid whose height is pinned to $0$ at the boundary.\nEach height is pulled towards the average height of its neighbours, and randomness pushes it away.\nLandscapes with large differences between neighbours are unlikely, so the surface is rough but not wild.\nThe discrete Gaussian free field is this random landscape, and its fine-mesh limit is the continuum free field.\n",
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