Berry–Esseen bound for operator norm of matrix averages

Question

Is there a Berry–Esseen bound for operator norm of an average of independent random matrices?
Suppose $A_1, dotsc, A_n$ are independent matrices with $mathbb{E}[A_i] = I$ (the identity matrix). Is there a Berry–Esseen bound for properly normalized $lVertoverline{A} - IrVert_text{op}$?

TOM · Answer

Check out this paper on Berry–Esseen inequalities for random vectors, maybe it will be useful:
Bentkus - On the dependence of the Berry–Esseen bound
on dimension.

Berry–Esseen bound for operator norm of matrix averages

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