Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Cuernavaca, México.
Centro Internacional de Ciencias, Cuernavaca, Mexico.
Sci Rep. 2017 Jan 17;7:40506. doi: 10.1038/srep40506.
It has been shown that, if a model displays long-range (power-law) spatial correlations, its equal-time correlation matrix will also have a power law tail in the distribution of its high-lying eigenvalues. The purpose of this paper is to show that the converse is generally incorrect: a power-law tail in the high-lying eigenvalues of the correlation matrix may exist even in the absence of equal-time power law correlations in the initial model. We may therefore view the study of the eigenvalue distribution of the correlation matrix as a more powerful tool than the study of spatial Correlations, one which may in fact uncover structure, that would otherwise not be apparent. Specifically, we show that in the Totally Asymmetric Simple Exclusion Process, whereas there are no clearly visible correlations in the steady state, the eigenvalues of its correlation matrix exhibit a rich structure which we describe in detail.
已经表明，如果一个模型显示出长程（幂律）空间相关性，那么它的等时相关矩阵在其高值特征值的分布中也将具有幂律尾部。本文的目的是表明，相反的情况通常是不正确的：即使初始模型中不存在等时幂律相关性，相关矩阵的高值特征值中也可能存在幂律尾部。因此，我们可以将研究相关矩阵的特征值分布视为比研究空间相关性更强大的工具，它实际上可能揭示出否则不明显的结构。具体来说，我们表明，在完全非对称简单排斥过程中，尽管在稳定状态下没有明显的相关性，但它的相关矩阵的特征值表现出我们详细描述的丰富结构。
