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A characterisation of the Gaussian free field

Probability Theory and Related Fields (2020) 176(3-4) 1259-1301
DOI: 10.1007/s00440-019-00939-9
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Abstract

We prove that a random distribution in two dimensions which is conformally invariant and satisfies a natural domain Markov property is a multiple of the Gaussian free field. This result holds subject only to a fourth moment assumption.

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Berestycki, N., Powell, E., & Ray, G. (2020). A characterisation of the Gaussian free field. Probability Theory and Related Fields, 176(3–4), 1259–1301. https://doi.org/10.1007/s00440-019-00939-9

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