\newcommand{\Str}{\operatorname{STr}} \newcommand{\Sdet}{\operatorname{SDet}} \newcommand{\Ber}{\operatorname{Ber}} \newcommand{\Cov}{\operatorname{Cov}} \newcommand{\IPR}{\operatorname{IPR}} \newcommand{\GUE}{\mathrm{GUE}} \newcommand{\Lref}{L} \newcommand{\Grass}[1]{{\textstyle\bigwedge}_{#1}} \newcommand{\Can}{\operatorname{Can}}