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Strong convergence of tensor products of independent G.U.E. matrices
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abstract
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.
Forward citations
Cited by 3 Pith papers
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