The discrete Gaussian free field on a compact manifold

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The discrete Gaussian free field on a compact manifold

Journal Article (2020)

Author(s)

Alessandra Cipriani (TU Delft - Electrical Engineering, Mathematics and Computer Science)

Bart van Ginkel (TU Delft - Electrical Engineering, Mathematics and Computer Science)

Research Group

Applied Probability

DOI related publication

https://doi.org/10.1016/j.spa.2019.11.005 Final published version

To reference this document use

https://resolver.tudelft.nl/uuid:258a4fa6-ce96-4a68-8db1-aa0b0b7c94fc

More Info

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Publication Year

2020

Language

English

Research Group

Applied Probability

Issue number

7

Volume number

130

Pages (from-to)

3943-3966

Downloads counter

202

Abstract

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 Z^d 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.