A simple proof of almost sure convergence for the largest singular value of a product of Gaussian matrices

Thiziri Nait Saada, Alireza Naderi

Let $m\ge 1$ and consider the product of $m$ independent $n\times n$ matrices $\mathbf{W}={\mathbf{W}}_1\dots {\mathbf{W}}_m$, each ${\mathbf{W}}_i$ with i.i.d. normalised $\math…