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arXiv · 2103.07273

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

Juhan Aru·Ellen Powell
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Abstract

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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Juhan Aru, Ellen Powell. 2021-03-12. A characterisation of the continuum Gaussian free field in $d \geq 2$ dimensions. https://arxiv.org/abs/2103.07273

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