The Driver-Hall-Kemp family of multiplicative Brownian motions on GL_N(C) strongly converges, almost surely and jointly with deterministic matrices, to the free multiplicative Brownian motion as N tends to infinity.
Extremal singular values of random matrix products and Brownian motion on GL(N, C)
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Strong Convergence of Multiplicative Brownian Motions on the General Linear Group
The Driver-Hall-Kemp family of multiplicative Brownian motions on GL_N(C) strongly converges, almost surely and jointly with deterministic matrices, to the free multiplicative Brownian motion as N tends to infinity.