论文标题
随机双分化图的全球特征值波动
Global eigenvalue fluctuations of random biregular bipartite graphs
论文作者
论文摘要
我们计算具有固定和生长程度的大量分析功能的均匀分布的随机双分配图的特征值波动。作为证明的关键步骤，我们在随机双折射两分图中获得了循环数量和周期性非背带步行的泊松近似值的总变化距离，这可能具有独立的利益。当$ \ frac {d_1} {d_2} {d_2} \ to \ infty $时，我们还证明了随机$（d_1，d_2）$的半圆定律（d_1，d_2）$。作为应用程序，我们将结果转化为均匀分布的随机常规超图的邻接矩阵。
We compute the eigenvalue fluctuations of uniformly distributed random biregular bipartite graphs with fixed and growing degrees for a large class of analytic functions. As a key step in the proof, we obtain a total variation distance bound for the Poisson approximation of the number of cycles and cyclically non-backtracking walks in random biregular bipartite graphs, which might be of independent interest. We also prove a semicircle law for random $(d_1,d_2)$-biregular bipartite graphs when $\frac{d_1}{d_2}\to\infty$. As an application, we translate the results to adjacency matrices of uniformly distributed random regular hypergraphs.
