4 problems

Classification conjecture. All sequences of polynomials satisfying $2m+1$-step relations of the precise form (0.5) are given by generalized periodic sequences of weights, together…

For any $u\in\{1,\ldots,N\}$, let $S^{u}_{xy}=\delta_{xy}S_{ux}$ and $S^{1/2,u}_{xy}=\delta_{xy}S^{1/2}_{ux}$. Let $G_s(z)$ be the resolvent, let $w_s$ be the associated spectral p…

Let $H$ be a one-dimensional band matrix of dimension $L$ and bandwidth $W$, and let $R=(H-z)^{-1}$ denote its resolvent. Resolvent decay conjecture. For $W\ll\sqrt{L}$, the $i,j$-…

Let $M$ be the real symmetric band random matrix defined by independent centered entries with variance $(1+\delta_{jk})\sigma^2$, normalized by $b_n^{-1/2}$, and band radius $b_n$.…