Probability, Curvature and Spectrum on Graphs

arXiv27 iulie 20261 min de cititArticolul și perspectiva sunt în engleză.

arXiv:2607.21639v1 Announce Type: cross Abstract: We show that, for a metric graph equipped with the Laplacian operator $\Delta=-\frac{d^2}{dx^2}$, 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.

Abstract:We show that, for a metric graph equipped with the Laplacian operator $\Delta=-\frac{d^2}{dx^2}$, 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.

Mathematical Physics (math-ph); Probability (math.PR); Spectral Theory (math.SP); Quantum Physics (quant-ph)

arXiv:2607.21639 [math-ph]

(or arXiv:2607.21639v1 [math-ph] for this version)

https://doi.org/10.48550/arXiv.2607.21639 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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