3 problems

Let $\hat{H}$ be a random matrix arising in a deep neural network, such as a positive-semidefinite curvature approximation, and let … be its Green's function. A local law is an app…

Local-law conjecture. Such a local law holds for all $\alpha\in(0,2)$ and for all intervals $I$ of length much larger than $1/n$.

The discussion concerns local eigenvalue statistics for random matrices with external source, where the global semicircle law need not describe the local behaviour. Local-law resil…