The discrete Gaussian free field on a compact manifold
| Autor: | Bart van Ginkel, Alessandra Cipriani |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
Random graph Continuum (topology) Euclidean space Applied Mathematics 010102 general mathematics Mathematical analysis Probability (math.PR) 01 natural sciences law.invention Sobolev space 010104 statistics & probability Scaling limit law Modeling and Simulation Gaussian free field FOS: Mathematics 0101 mathematics Voronoi diagram Manifold (fluid mechanics) Mathematics - Probability Mathematics |
| ISSN: | 0304-4149 |
| DOI: | 10.48550/arxiv.1809.03382 |
| Popis: | In this article we aim at defining 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 $\mathbb{Z}^d$ 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. Comment: 21 pages, minor changes, accepted for publication in Stochastic Processes and their Applications (available at https://www.sciencedirect.com/science/article/pii/S0304414919301310) |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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