18 problems

Let $\boldsymbol{H}_N\boldsymbol{H}_N^\dagger$ be a finite-band random Hermitian matrix constructed from random entries. Entry-distribution dependence conjecture. The limiting spec…

Let $k$ be a positive integer and let … where, for every $i,j=1,\dots,k$, $f_{i,j}\in L^{\infty}([-i,i]])$ is real-valued almost everywhere, and either $T_n(f_{i,j})$ is Hermitian…

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

Let $\{X_n\}_n$ and $\{Y_n\}_n$ be matrix-sequences with $X_n,Y_n\in\mathbb C^{d_n\times d_n}$. Assume that $X_n$ is Hermitian for all $n$ and $\{X_n\}_n\sim_{\lambda}f$, where $f$…

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…

Diagonal embedding conjecture. Any algebra $\mathfrak A\subseteq\mathfrak C_D$ embeds into $\mathfrak D$: there exist a sequence of unitary matrices $\{U_n\}_n$ and an isomorphism…

Universal GLT algebra embedding conjecture. Any algebra $\mathfrak A\subseteq\mathfrak C_D$ embeds into $\mathfrak G$: there exists a sequence of unitary matrices $\{U_n\}_n$ such…

Universal GLT group embedding conjecture. Any group $d524\mathfrak A\subseteqd524\mathfrak C_D$ embeds into $d524\mathfrak G$: there exist sequences of unitary matrices $\{U_n\}_n$…

A frame is sampled by selecting typical $k$-submatrices, and the resulting spectral distribution is compared with the limiting MANOVA distribution. Farrell's conjecture. The phenom…

Bordenave's conjecture. The empirical spectral distribution of $A_n$ converges, as $n\to\infty$, to a measure $\mu_d$ on the complex plane whose density with respect to Lebesgue me…

Let $X=(X_{ij})_{i,j=1,\ldots,n}$ be a uniformly chosen doubly stochastic matrix, and set … The empirical spectral distribution of $\bar{X}$ is the probability measure assigning ma…

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…

Let a finite-band random matrix be compared with a full random matrix, and consider the limiting spectrum as the matrix size tends to infinity. Finite-band distribution-dependence…

Consider finite-band random Hermitian matrices whose entries are determined by fading coefficients, and let the limiting moments be computed from the moments of the fading amplitud…

Consider the infinite linear Wyner model with $\beta=\alpha$, $\pi_a=\pi_b=\pi_c=\pi$, and $K=1$, and let $\boldsymbol{H}_N$ denote its channel matrix. The unordered eigenvalue dis…