Local Kesten–McKay Law for Random Regular Graphs
Local Kesten–McKay Law for Random Regular Graphs
We study the adjacency matrices of random d-regular graphs with large but fixed degree d. In the bulk of the spectrum $${[-2\sqrt{d-1}+\varepsilon, 2\sqrt{d-1}-\varepsilon]}$$ down to the optimal spectral scale, we prove that the Green's functions can be approximated by those of certain infinite tree-like (few cycles) graphs that depend only …