8 problems

An ensemble of random matrices $A^N$ has independent centered $L^2$ entries, each with variance $1/N$. Girko's circular law conjecture. The empirical measure of the eigenvalues of…

Let $X_n$ be an $n\times n$ random matrix with independent and identically distributed entries having mean $0$ and variance $1/n$. Let $\rho(z)$ denote the limiting eigenvalue dens…

Let $A_n=(a_{ij})$ and $B_n=(b_{ij})$ be independent real $n\times n$ matrices with i.i.d. entries satisfying … and assume a standard moment condition strong enough to imply the ci…

Missing-data circular-law conjecture. The limiting spectral distribution of $n^{-1/2}D_n\odot X_n$ is the uniform probability measure on the unit disk almost surely if and only if…

Fix $\alpha \in [0,1)$. Let $A=PLQ$ be an $n\times n$ random matrix, where $P$ and $Q$ are independent uniformly chosen permutation matrices and $L$ is independent of $P$ and $Q$.…

Let $A_n$ be a uniformly random element of the set of adjacency matrices of $d$-regular directed graphs on $n$ vertices, and let $\frac{1}{\sqrt d}A_n$ have empirical spectral dist…

Bordenave–Caputo–Chafaï–Tikhomirov conjecture. The convergence in probability

Let $M_n$ be the $n \times n$ random matrix whose entries are iid complex random variables with mean 0 and variance 1. The empirical spectral distribution (ESD) of…