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.

45 pages, 5 figures, minor revision

References in corpus (4)

• Exchangeable pairs and Poisson approximation
• ${\ell }_p$-Spread and Restricted Isometry Properties of Sparse Random Matrices
• CLT for linear spectral statistics of normalized sample covariance matrices with the dimension much larger than the sample size
• The spectral density of dense random networks and the breakdown of the Wigner semicircle law

Cited by in corpus (1)

• On the second eigenvalue of random bipartite biregular graphs