AI 中文总结
研究图上概率、曲率和谱的关系，基于受威尔逊线和全同性启发的图曲率概念及冯·诺依曼遍历定理，为配备特定拉普拉斯算子的度量图的图迹公式给出新解释。
AI 中文摘要
我们表明，对于配备拉普拉斯算子Δ = -d²/dx²的度量图，图迹公式在量子概率和曲率方面有新解释。我们的方法基于受威尔逊线和全同性启发的图曲率概念以及冯·诺依曼遍历定理。
英文摘要
We show that, for a metric graph equipped with the Laplacian operator $Δ=-\frac{d^2}{dx^2}$, 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.
