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

Abstract

We prove that under certain mild moment and continuity assumptions, the $d$-dimensional Gaussian free field is the only stochastic process in $d\ge 2$ 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.

Some small imprecisions and typos that were discovered in the published version are corrected; still no figures

References in corpus (1)

• Lecture notes on the Gaussian Free Field