Range-Renewal Processes: SLLN, Power Law and Beyonds
Probability
2013-12-12 v2 Statistics Theory
Statistics Theory
Abstract
Given samples of a regular discrete distribution , we prove in this article first a serial of SLLNs results (of Dvoretzky and Erd\"{o}s' type) which implies a typical power law when is heavy-tailed. Constructing a (random) graph from the ordered samples, we can establish other laws for the degree-distribution of the graph. The phenomena of small world is also discussed.
Cite
@article{arxiv.1305.1829,
title = {Range-Renewal Processes: SLLN, Power Law and Beyonds},
author = {Xin-Xing Chen and Jian-Sheng Xie and Jiangang Ying},
journal= {arXiv preprint arXiv:1305.1829},
year = {2013}
}
Comments
28 pages