7 problems

Circular-law universality conjecture. For constant linear margins and every base measure $\mu$ satisfying the hypothesis of Corollary, the empirical eigenvalue distribution of

Non-sub-Gaussian ESD conjecture. The conclusion of Theorem (ii) holds without assuming that the base measure $\mu$ is sub-Gaussian.

Let $k$ be an even, non-negative, bounded, compactly supported measurable function with $\\|k\\|_1=1$, supported on $[-1,1]$, and let $L(x)$ be strictly positive on $[0,1]$. Define…

Real-part spectral-symbol conjecture. Is it true that

Small trace-norm perturbation conjecture. Then

Common-unitary normal-form conjecture. Any algebra $\mathfrak A\subseteq\mathfrak C_D$ induced by such $\mathscr A$ and $s$ admits a unitary sequence $\{U_n\}_n$ such that…

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…