Bulk universality and quantum unique ergodicity for random band matrices in high dimensions

Changji Xu, Fan Yang, Horng-Tzer Yau +1

We consider Hermitian random band matrices $H=(h_{xy})$ on the $d$-dimensional lattice $(\mathbb{Z}/L\mathbb{Z}{)}^d$, where the entries $h_{xy}={\overline{h}}_{yx}$ are independent cent…