论文标题
跨越树木，跨循环跨越森林，扁平表面和分析扭转的森林
Spanning trees, cycle-rooted spanning forests on discretizations of flat surfaces and analytic torsion
论文作者
论文摘要
我们研究了与半翻译表面的离散化相关的图形拉普拉斯的决定因素的渐近膨胀，并具有平坦的单一载体束。通过这样做，通过离散化，我们将跨越树木数量的渐近膨胀以及由单位矢量束的连接的单型膜加权的循环根源跨越森林的总和与相应的Zeta Zeta调控确定归因。 作为一种应用，通过将我们的结果与Kassel-Kenyon的最新作品相结合，Modulo一些普遍的拓扑常数，我们给出了明确的公式，以限制具有循环根源的跨越森林，并具有不可扣除的循环，并在给定的表面上均匀地采样，以其cycles诱导其cycles cycles cycles均匀地采样。我们还计算了相关循环测量中某些拓扑可观察物的极限的明确值。
We study the asymptotic expansion of the determinant of the graph Laplacian associated to discretizations of a half-translation surface endowed with a flat unitary vector bundle. By doing so, over the discretizations, we relate the asymptotic expansion of the number of spanning trees and the sum of cycle-rooted spanning forests weighted by the monodromy of the connection of the unitary vector bundle, to the corresponding zeta-regularized determinants. As one application, by combining our result with a recent work of Kassel-Kenyon, modulo some universal topological constants, we give an explicit formula for the limit of the probability that a cycle-rooted spanning forest with non-contractible loops, sampled uniformly on discretizations approaching a given surface, induces the given lamination by its cycles. We also calculate an explicit value for the limit of certain topological observables on the associated loop measures.
