论文标题
磁性图
Isoperimetric and Sobolev inequalities for magnetic graphs
论文作者
论文摘要
我们介绍了用于磁性图的等值尺寸的概念，即每个边缘分配一个复杂数量的模量的概念。与经典案例类似，我们表明等仪不平等意味着Sobolev在此类图上的不平等现象。作为第一个应用程序，我们表明，签名的Cheeger常数相对于笛卡尔产品的图形产生了添加性。使用热内核技术，我们还为离散磁拉曲板的特征值提供了下限。
We introduce a concept of isoperimetric dimension for magnetic graphs, that is, graphs where every edge is assigned a complex number of modulus one. In analogy with the classical case, we show that isoperimetric inequalities imply Sobolev inequalities on such graphs. As a first application, we show that the signed Cheeger constant behaves additively with respect to Cartesian products of graphs. Using heat kernel techniques, we also give lower bounds for the eigenvalues of the discrete magnetic Laplacian.
