独立 G.U.E. 矩阵张量积的强收敛

Serban Belinschi; Mireille Capitaine

独立 G.U.E. 矩阵张量积的强收敛

算子代数 2024-01-31 v2 概率论

作者: Serban Belinschi , Mireille Capitaine

摘要

给定适当归一化的独立 $N\times N$ G.U.E. 矩阵组 $(X_N^{(1)},\dots,X_N^{(r_1)})$ 与 $(Y_N^{(1)},\dots,Y_N^{(r_2)})$ ,我们证明当 $N$ 趋于无穷时, $N^2\times N^2$ 随机矩阵组 $(X_N^{(1)}\otimes I_N,\dots,X_N^{(r_1)}\otimes I_N,I_N\otimes Y_N^{(1)},\dots,I_N\otimes Y_N^{(r_2)})$ 强收敛。Ben Hayes 已证明该结果蕴含 Peterson-Thom 猜想成立。

关键词

张量积 G.U.E. 矩阵强收敛随机矩阵 Peterson-Thom 猜想

引用

@article{arxiv.2205.07695,
  title  = {Strong convergence of tensor products of independent G.U.E. matrices},
  author = {Serban Belinschi and Mireille Capitaine},
  journal= {arXiv preprint arXiv:2205.07695},
  year   = {2024}
}

备注

Second, longer version, providing explicit calculations for the application of the flip and the partial difference-differential on resolvents of tensor products of operators. The reader comfortable with free noncommutative functions theory might benefit more from reading the first version

独立 G.U.E. 矩阵张量积的强收敛

摘要

关键词

引用

备注

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