伪分形无标度网首次穿越性质的精确计算
Exact calculations of first-passage properties on the pseudofractal scale-free web
摘要：
本文研究了伪分形无标度网上的离散时间随机游动，并分析了相关的首次通过性质。首先，我们将PSFW的节点分为不同的层次，并提出了一种方法来推导从任意起始节点到吸收域的第一次通过概率的生成函数，该吸收域位于低层次的一个或多个节点（即，节点度大）。然后，我们利用生成函数作为工具，精确地计算了首达概率、生存概率、首达时间的均值和方差。最后，对于一些说明性的例子，对应于给定的选择的起始节点和吸收域，我们得到精确和明确的结果，这样的首次通过性能。我们提出的方法同样可以解决吸收域位于PSFW上一个或多个高层节点的情况，也可以用于计算其他具有自相似结构的网络，如$(u, v)$花和递归无标度树的首次通过性质.
英文摘要：
In this paper, we consider discrete time random walks on the pseudofractal scale-free web (PSFW) and we study analytically the related first passage properties. First, we classify the nodes of the PSFW into different levels and propose a method to derive the generation function of the first passage probability from an arbitrary starting node to the absorbing domain, which is located at one or more nodes of low-level (i.e., nodes with large degree). Then, we calculate exactly the first passage probability, the survival probability, the mean and the variance of first passage time by using the generating functions as a tool. Finally, for some illustrative examples corresponding to given choices of starting node and absorbing domain, we derive exact and explicit results for such first passage properties. The method we propose can as well address the cases where the absorbing domain is located at one or more nodes of high-level on the PSFW, and it can also be used to calculate the first passage properties on other networks with self-similar structure, such as $(u, v)$ flowers and recursive scale-free trees.
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