2026/07/21 by Tianhong Zhao
#math-ph #math.MP #math.PR #math.SP #quant-ph
We show that, for a metric graph equipped with the Laplacian operator Δ=-(d2)/(dx2), 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.