Full eigenvalues of the Markov matrix for scale-free polymer networks.
Full eigenvalues of the Markov matrix for scale-free polymer networks.
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DOI：
10.1103/physreve.90.022816
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发表时间：
2014-08
期刊：
影响因子：
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通讯作者：
Zhongzhi Zhang;Xiaoye Guo;Yuan Lin
中科院分区：
文献类型：
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作者：
Zhongzhi Zhang;Xiaoye Guo;Yuan Lin
谱方法是复杂系统分析中不可缺少的重要工具，它可以从随机游动的Markov矩阵的特征值和特征向量中提取有关复杂系统结构和动力学性质的重要信息。本文研究了一类无标度聚合物网络的马尔可夫矩阵。我们提出了一个精确的解析表达式的所有特征值，并明确确定其多重性。然后，我们使用所获得的特征值，推导出一个明确的随机目标访问时间的随机游动的研究网络上的公式。此外，基于马尔可夫矩阵的特征值和生成树的数目之间的联系，我们证实了所获得的特征值及其相应的退化的有效性。
Much important information about the structural and dynamical properties of complex systems can be extracted from the eigenvalues and eigenvectors of a Markov matrix associated with random walks performed on these systems, and spectral methods have become an indispensable tool in the complex system analysis. In this paper, we study the Markov matrix of a class of scale-free polymer networks. We present an exact analytical expression for all the eigenvalues and determine explicitly their multiplicities. We then use the obtained eigenvalues to derive an explicit formula for the random target access time for random walks on the studied networks. Furthermore, based on the link between the eigenvalues of the Markov matrix and the number of spanning trees, we confirm the validity of the obtained eigenvalues and their corresponding degeneracies.