Berestycki, NathanaëlPowell, EllenRay, Gourab2025-02-192025-02-192019Berestycki, N., Powell, E., & Ray, G. (2019). A characterisation of the Gaussian free field. Probability Theory and Related Fields, 176(3–4), 1259–1301. https://doi.org/10.1007/s00440-019-00939-9https://doi.org/10.1007/s00440-019-00939-9https://hdl.handle.net/1828/21217We 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.enAttribution 4.0 InternationalArticleDepartment of Mathematics and Statistics