  Given tuples of properly normalized independent $N\times N$ G.U.E. matrices
$(X_N^{(1)},\dots,X_N^{(r_1)})$ and $(Y_N^{(1)},\dots,Y_N^{(r_2)})$, we show
that the tuple $(X_N^{(1)}\otimes I_N,\dots,X_N^{(r_1)}\otimes I_N,I_N\otimes
Y_N^{(1)},\dots,I_N\otimes Y_N^{(r_2)})$ of $N^2\times N^2$ random matrices
converges strongly as $N$ tends to infinity. It was shown by Ben Hayes that
this result implies that the Peterson-Thom conjecture is true.
