论文标题
离散的拉普拉斯和过渡运算符在非Archimedean有序字段上
Discrete Laplace and transition operators over non-Archimedean ordered fields
论文作者
论文摘要
我们研究了非架构有限的字段上有限图的归一化laplacian $ \ Mathcal l $频谱的属性。我们证明了第一个非零特征值的cheeger不平等。然后，我们描述运算符$ \ MATHCAL P = I- \ MATHCAL L $的属性，这是过渡操作员的概括。我们表明，Cheeger估计$α_1\ prepeq \ sqrt {1-h^2} $对于$ \ Mathcal P $的第二大特征值对于研究非架构订购的领域的随机步行对等于平衡的类似物的融合至关重要。我们考虑了Levi-Civita领域的例子。
We investigate properties of spectrum of normalized Laplacian $\mathcal L$ for finite graphs over non-Archimedean ordered fields. We prove a Cheeger's inequality for first non-zero eigenvalue. Then we describe properties of the operator $\mathcal P=I-\mathcal L$, which is a generalization of transition operator. We show that Cheeger estimate $α_1\preceq \sqrt{1-h^2}$ for the second largest eigenvalue of $\mathcal P$ is crucial for investigation of the convergence of analogue of random walk to equilibrium over a non-Archimedean ordered fields. We consider examples over the Levi-Civita field.
