TY - JOUR
T1 - The discrete Gaussian free field on a compact manifold
AU - Cipriani, Alessandra
AU - van Ginkel, Bart
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85076241576&partnerID=8YFLogxK
U2 - 10.1016/j.spa.2019.11.005
DO - 10.1016/j.spa.2019.11.005
M3 - Article
AN - SCOPUS:85076241576
SN - 0304-4149
VL - 130
SP - 3943
EP - 3966
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 7
ER -