Exterior-Interior Duality for Discrete Graphs

Details Exterior-Interior Duality for Discrete Graphs Exterior-Interior Duality for Discrete Graphs

2008-11-13

arxiv.org/abs/0811.2032v1

Physics

Mathematical Physics

15 pages 1 figure

Scientific paper

10.1088/1751-8113/42/3/035101

The Exterior-Interior duality expresses a deep connection between the Laplace spectrum in bounded and connected domains in $\mathbb{R}^2$, and the scattering matrices in the exterior of the domains. Here, this link is extended to the study of the spectrum of the discrete Laplacian on finite graphs. For this purpose, two methods are devised for associating scattering matrices to the graphs. The Exterior -Interior duality is derived for both methods.

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