Generating Functions of Waiting Times and Numbers of Visits for Random Walks on Graphs
Generating Functions of Waiting Times and Numbers of Visits for Random Walks on Graphs
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DOI：
10.1007/s11009-011-9246-7
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发表时间：
2011-08
影响因子：
0.9
通讯作者：
K. Inoue;S. Aki;Balakrishnan Narayanaswamy
中科院分区：
文献类型：
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作者：
K. Inoue;S. Aki;Balakrishnan Narayanaswamy
在这篇文章中，我们考虑了图上随机游动的覆盖时间问题。通过使用生成函数，我们提出了一个统一的方法来研究与等待时间的分布。此外，还研究了图上随机游动的访问次数的分布。我们提出的等待时间和访问次数的分布之间的关系。我们还表明，这些理论结果可以很容易地通过一些计算机代数系统进行，并提出了一些数值结果的覆盖时间，以证明开发的结果的有用性。最后，利用生成函数研究覆盖时间问题，得到了更广泛的发展。
In this paper, we consider some cover time problems for random walks on graphs in a wide class of waiting time problems. By using generating functions, we present a unified approach for the study of distributions associated with waiting times. In addition, the distributions of the numbers of visits for the random walks on the graphs are also studied. We present the relationship between the distributions of the waiting times and the numbers of visits. We also show that these theoretical results can be easily carried out through some computer algebra systems and present some numerical results for cover times in order to demonstrate the usefulness of the results developed. Finally, the study of cover time problems through generating functions leads to more extensive development.