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 2kth moment of the limit equals a weighted sum over different types of pair-partitions of the set {1, 2,…, 2k} and are universal. Some results are also known for the sparse case. In this paper, we generalize 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.

中文翻译：

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一些具有独立条目的模式矩阵

反向循环、对称循环、Toeplitz 和 Hankel 矩阵等图案化随机矩阵及其几乎确定的极限谱分布（LSD）引起了广泛关注。在条目取自具有有限方差的独立同分布序列的假设下，LSD 由一个公共线程捆绑在一起——2ķ极限的时刻等于集合的不同类型对分区的加权和{1, 2,…, 2ķ}并且是通用的。一些结果也因稀疏情况而闻名。在本文中，我们通过显着放宽独立同分布假设来概括这些结果。对于我们的模型，限制是通过更大类别的分区定义的，也不是通用的。一些现有的和新的模式矩阵的结果，它们的带和稀疏版本，以及具有连续和离散方差分布的矩阵作为特殊情况。