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.

中文翻译：

---

随机双正则二部图的全局特征值涨落

我们计算一大类解析函数的具有固定度和增长度的均匀分布随机双正则二分图的特征值波动。作为证明中的关键步骤，我们获得了随机双正则二部图中循环数和循环非回溯游走的泊松近似的总变化距离界限，这可能是独立的兴趣。我们还证明了随机数的半圆定律$（d_1,d_2）$-双正则二部图当$\frac{d_1}{d_2}\to \mathrm{无穷大}$。作为一个应用程序，我们将结果转换为均匀分布的随机正则超图的邻接矩阵。