2 problems

Let $A$ be a random real symmetric banded matrix of size $N\times N$ with independent entries and bandwidth $b\asymp N^\alpha$. Poisson/Gaudin–Mehta conjecture. The limiting local…

Let a permutation matrix have bandwidth $w$, meaning that its nonzero entries lie within $w$ diagonals of the main diagonal. A bandwidth-$1$ permutation is a product of mutually no…