论文标题
一些带有独立条目的图案矩阵
Some patterned matrices with independent entries
论文作者
论文摘要
图案化的随机矩阵，例如反向循环器，对称循环液，Toeplitz和Hankel矩阵及其几乎确定的限制光谱分布（LSD），引起了很多关注。假设条目取自I.I.D.具有有限差异的序列，LSD由一个共同的线程绑定在一起 - 极限的$ 2K $ TH时刻等于集合的加权总和，以$ \ {1，2，\ ldots，2k \} $和通用。一些结果也因稀疏情况而闻名。在本文中，我们通过显着放松I.I.D.来概括这些结果。假设。对于我们的模型，限制是通过较大的分区来定义的，并且也不通用。具有图案的矩阵，它们的频段和稀疏版本以及具有连续和离散差异的矩阵的几个现有和新的结果。
Patterned random matrices such as the reverse circulant, the symmetric circulant, the Toeplitz and the Hankel matrices and their almost sure limiting spectral distribution (LSD), have attracted much attention. Under the assumption that the entries are taken from an i.i.d. sequence with finite variance, the LSD are tied together by a common thread -- the $2k$th moment of the limit equals a weighted sum over different types of pair-partitions of the set $\{1, 2, \ldots, 2k\}$ and are universal. Some results are also known for the sparse case. In this paper we generalise these results by relaxing significantly the i.i.d. assumption. For our models, the limits are defined via a larger class of partitions and are also not universal. Several existing and new results for patterned matrices, their band and sparse versions, as well as for matrices with continuous and discrete variance profile follow as special cases.
