Harmonic deformation of Delaunay triangulations
Pablo A. Ferrari, Rafael M. Grisi, Pablo Groisman
TL;DR
This paper introduces a method to construct harmonic functions on Delaunay triangulations derived from ergodic point processes by utilizing the zero-temperature harness process, advancing understanding of harmonic analysis on random geometric graphs.
Contribution
It presents a novel approach to defining harmonic functions on Delaunay triangulations through the zero-temperature harness process, linking stochastic geometry with harmonic analysis.
Findings
Harmonic functions can be obtained as limits of the harness process on Delaunay triangulations.
The method applies to ergodic point processes, broadening the scope of harmonic analysis on random graphs.
The approach provides new insights into the structure of harmonic functions in stochastic geometric settings.
Abstract
We construct harmonic functions on random graphs given by Delaunay triangulations of ergodic point processes as the limit of the zero-temperature harness process.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Data Management and Algorithms · Computational Geometry and Mesh Generation