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arXiv · 1205.1123

Operators of rank 1, discrete path integration and graph Laplacians

Yurii M. Burman
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Abstract

We prove a formula for a characteristic polynomial of an operator expressed as a polynomial of rank 1 operators. The formula uses a discrete analog of path integration and implies a generalization of the Forman-Kenyon's formula [4,6] for a determinant of the graph Laplacian (which, in its turn, implies the famous matrix-tree theorem by Kirchhoff) as well as its level 2 analog, where the summation is performed over triangulated nodal surfaces with boundary.

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Yurii M. Burman. 2012-09-09. Operators of rank 1, discrete path integration and graph Laplacians. https://arxiv.org/abs/1205.1123

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