2 problems

Consider random band matrices with non-periodic variance profiles, including i.i.d. entries and general profile functions, in the regime $1\ll W\ll L$. Let Theorems … denote the ma…

For the harmonic oscillator $V(x)=\frac{1}{2}x^2$, let $x^+=\sqrt{\beta N}$ be the right edge and let $w_N=\frac{\sqrt{\beta}}{2}N^{-1/6}$ be the width of the edge region. For…