Title: Bulk Eigenvalue Correlation Statistics of Random Biregular Bipartite Graphs,
Abstract: This paper is the second chapter of three of the author's undergraduate
thesis. In this paper, we consider the random matrix ensemble given by $(d_b,
d_w)$-regular graphs on $M$ black vertices and $N$ white vertices, where $d_b
\in [N^{\gamma}, N^{2/3 - \gamma}]$ for any $\gamma > 0$. We simultaneously
prove that the bulk eigenvalue correlation statistics for both normalized
adjacency matrices and their corresponding covariance matrices are stable for
short times. Combined with an ergodicity analysis of the Dyson Brownian motion
in another paper, this proves universality of bulk eigenvalue correlation
statistics, matching normalized adjacency matrices with the GOE and the
corresponding covariance matrices with the Gaussian Wishart Ensemble.