论文标题
独立G.U.E.张量的强烈收敛性矩阵
Strong convergence of tensor products of independent G.U.E. matrices
论文作者
论文摘要
给定适当标准化的独立$ n \ times n $ g.u.e.的元组矩阵$（x_n^{（1）}，\ dots，x_n^{（r_1）}）$和$（y_n^{（1）}，\ dots，y_n^{（r_2）}）$ i_n，\ dots，x_n^{（r_1）} \ otimes i_n，i_n \ otimes y_n^{（1）}，\ dots，i_n \ otimes y_n^{（r_2）} $ n^2 \ times n^2 \ times n^2 \ times n^times n^2 $随机n^2 $ toxtric in Infinity in Infinity Inf ingity in Infine in Inf in Inf。本·海耶斯（Ben Hayes）表明，这一结果暗示了彼得森 - 本姆猜想是正确的。
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.
