论文标题
渐近$ \ ast $ - 分配排列的HAAR统一矩阵
Asymptotic $\ast$--distribution of permuted Haar unitary matrices
论文作者
论文摘要
我们研究带有置换条目的HAAR统一随机矩阵。对于一系列排列$ \ left（σ_n\右）_n $，其中$σ_n$作用于$ n \ times n $矩阵，我们确定了$ \ ast $ - 分配排列的haar单位矩阵$ u_n^=σ_n} $的条件是循环和commptary coundermutal and perper $ umemmed $ umemmnn $。我们证明这种收敛是在几乎确定的意义上发生的。此外，我们表明，我们对排列顺序的条件在几乎可以通过一系列随机排列来满足的意义上是通用的。
We study Haar unitary random matrices with permuted entries. For a sequence of permutations $\left(σ_N\right)_N$, where $σ_N$ acts on $N\times N$ matrices we identify conditions under which the $\ast$--distribution of permuted Haar unitary matrices $U_N^{σ_N}$ is asymptotically circular and free from the unpermuted sequence $U_N$. We show that this convergence takes place in the almost sure sense. Moreover we show that our conditions on the sequence of permutations are generic in the sense that are almost surely satisfied by a sequence of random permutations.
