The discrete Gaussian free field on a compact manifold

Alessandra Cipriani*, Bart van Ginkel

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)


In this article we define the discrete Gaussian free field (DGFF) on a compact manifold. Since there is no canonical grid approximation of a manifold, we construct a random graph that suitably replaces the square lattice Zd in Euclidean space, and prove that the scaling limit of the DGFF is given by the manifold continuum Gaussian free field (GFF). Furthermore using Voronoi tessellations we can interpret the DGFF as element of a Sobolev space and show convergence to the GFF in law with respect to the strong Sobolev topology.

Original languageEnglish
Pages (from-to)3943-3966
Number of pages24
JournalStochastic Processes and their Applications
Issue number7
Publication statusPublished - 2020


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