13 citations · 29 across the 7 of their papers we have counts for
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Size of nodal domains of the eigenvectors of a G(n,p) graph
Han Huang, Mark Rudelson
Consider an eigenvector of the adjacency matrix of a G(n, p) graph. A nodal domain is a connected component of the set of vertices where this eigenvector has a constant sign. It is…
Sharp transition of the invertibility of the adjacency matrices of sparse random graphs
Anirban Basak, Mark Rudelson
We consider three different models of sparse random graphs:~undirected and directed Erdős-Rényi graphs, and random bipartite graph with an equal number of left and right vertices.…
The sparse circular law under minimal assumptions
Mark Rudelson, Konstantin Tikhomirov
The circular law asserts that the empirical distribution of eigenvalues of appropriately normalized matrix with i.i.d. entries converges to the uniform measure on the u…
Delocalization of eigenvectors of random matrices. Lecture notes
Mark Rudelson
Let be a unit eigenvector of an random matrix. This vector is delocalized if it is distributed roughly uniformly over the real or complex sphere. This…