论文标题
在有向网络上的非本地偏见随机步行和分数运输
Nonlocal biased random walks and fractional transport on directed networks
论文作者
论文摘要
In this paper, we study nonlocal random walk strategies generated with the fractional Laplacian matrix of directed networks.我们提出了一种通用方法，通过将动态定义为离散时间的马尔可夫过程来分析这些策略，该过程以laplacian矩阵的力量表示的节点之间的过渡概率。我们分析了过渡矩阵及其各自的特征值和特征向量的要素，平均第一个通行时间和全球时间以表征随机行走策略。 We apply this approach to the study of particular local and nonlocal ergodic random walks on different directed networks; we explore circulant networks, the biased transport on rings and the dynamics on random networks. We study the efficiency of a fractional random walker with bias on these structures. Effects of ergodicity loss which occur when a directed network is not any more strongly connected are also discussed.
In this paper, we study nonlocal random walk strategies generated with the fractional Laplacian matrix of directed networks. We present a general approach to analyzing these strategies by defining the dynamics as a discrete-time Markovian process with transition probabilities between nodes expressed in terms of powers of the Laplacian matrix. We analyze the elements of the transition matrices and their respective eigenvalues and eigenvectors, the mean first passage times and global times to characterize the random walk strategies. We apply this approach to the study of particular local and nonlocal ergodic random walks on different directed networks; we explore circulant networks, the biased transport on rings and the dynamics on random networks. We study the efficiency of a fractional random walker with bias on these structures. Effects of ergodicity loss which occur when a directed network is not any more strongly connected are also discussed.
