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A characterisation of the continuum Gaussian free field in d \geq 2 dimensions

Juhan Aru, Ellen Powell

12/3/21 Published in : arXiv:2103.07273

We prove that under certain mild moment and continuity assumptions, the d-dimensional Gaussian free field is the only stochastic process in d\geq 2 that is translation invariant, exhibits a certain scaling, and satisfies the usual domain Markov property. Our proof is based on a decomposition of the underlying functional space in terms of radial processes and spherical harmonics.

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Correlations of primary fields in the critical Ising model

Closed string deformations in open string field theory II: superstring

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