Global eigenvalue fluctuations of random biregular bipartite graphs

We compute the eigenvalue fluctuations of uniformly distributed random biregular bipartite graphs with fixed and growing degrees for a large class analytic functions. As key step in proof, we obtain total variation distance bound Poisson approximation number cycles cyclically non-backtracking walks graphs, which might be independent interest. also prove semicircle law [Formula: see text]-biregular when text]. an application, translate results to adjacency matrices regular hypergraphs.