On the range of random walk on graphs satisfying a uniform condition
Probability
2014-07-28 v2
Abstract
We consider the range of random walks up to time n, R_n, on graphs satisfying a uniform condition. This condition is characterized by potential theory. Not only all vertex transitive graphs but also many non-regular graphs satisfy the condition. We show certain weak laws of R_n from above and below. We also show that there is a graph such that it satisfies the condition and a sequence of the mean of R_n/n fluctuates. By noting the construction of the graph, we see that under the condition, the weak laws are best in a sense.
Keywords
Cite
@article{arxiv.1308.1487,
title = {On the range of random walk on graphs satisfying a uniform condition},
author = {Kazuki Okamura},
journal= {arXiv preprint arXiv:1308.1487},
year = {2014}
}
Comments
21 pages, Section for Examples rewritten