Local Marchenko-Pastur Law for Random Bipartite Graphs

Understand

This paper is the first chapter of three of the author's undergraduate thesis.

• We study the random matrix ensemble of covariance matrices arising from random $(d_b, d_w)$-regular bipartite graphs on a set of $M$ black vertices and $N$ white vertices, for $d_b \gg \log^4 N$.
• We simultaneously prove that the Green's functions of these covariance matrices and the adjacency matrices of the underlying graphs agree with the corresponding limiting law (e.g.
• Marchenko-Pastur law for covariance matrices) down to the optimal scale.