Probability, Curvature and Spectrum on Graphs
Tianhong Zhao
Abstract
We show that, for a metric graph equipped with the Laplacian operator Δ=-d2dx2, the graph trace formula admits a new interpretation in terms of quantum probability and curvature. Our approach is based on a notion of graph curvature inspired by Wilson-lines and holonomy, together with von-Neumann's ergodic theorem.
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