A Sudakov--Fernique proof of Lehner-type edge bounds for matrix-valued GUE sums

Benoit Collins, Yuta Yamagishi

Let $A_0,A_1,\dots ,A_n\in M_N(\mathbb{C})$ be Hermitian matrices and let $G_1,\dots ,G_n$ be independent $M\times M$ GUE matrices normalized so that $\Vert M^{-1/2}{G}_i\Vert \to 2$ almost…