Global eigenvalue fluctuations of random biregular bipartite graphs

Abstract

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.

arXiv comment45 pages, 5 figures, minor revision

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Cited by in corpus (1)

• On the second eigenvalue of random bipartite biregular graphs