模糊 Erdős–Rényi 随机图：谱统计
Fuzzy Erdos-Renyi random graphs: Spectral statistics
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中文总结 AI 辅助
该研究在随机矩阵理论框架下数值研究模糊 Erdős–Rényi 随机图的谱统计，发现平均度是控制其谱性质的标度参数。
中文摘要 AI 辅助
在随机矩阵理论（RMT）框架内，我们对模糊 Erdős–Rényi（ER）随机图的谱统计进行了详细的数值研究。具体而言，我们将模糊 ER 图模型中顶点和边的隶属度视为随机变量。由此，相应的邻接矩阵成为具有随机元素的稀疏矩阵。随后，我们应用标准 RMT 度量来表征无向和有向模糊图的厄米与非厄米邻接矩阵系综的特征值和特征向量。我们证明，ER 模型的平均度可作为相应模糊设置谱性质的标度参数。
英文摘要
Within a random-matrix-theory (RMT) approach, we perform a detailed numerical study of the spectral statistics of fuzzy Erdos-Renyi (ER) random graphs. Specifically, we consider the membership values of the vertices and edges of a fuzzy ER graph model as random variables. In this way, the corresponding adjacency matrices become sparse matrices with random entries. Then, we apply standard RMT measures to characterize the eigenvalues and eigenvectors of ensembles of Hermitian and non-Hermitian adjacency matrices of both undirected and directed fuzzy graphs. We demonstrate that the average degree of the ER model serves as the scaling parameter of the spectral properties of the corresponding fuzzy setups.
发表机构
- Instituto de Física, Benemérita Universidad Autónoma de Puebla（普埃布拉自治大学物理研究所）
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