English

Range-Renewal Processes: SLLN, Power Law and Beyonds

Probability 2013-12-12 v2 Statistics Theory Statistics Theory

Abstract

Given nn samples of a regular discrete distribution π\pi, 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 π\pi is heavy-tailed. Constructing a (random) graph from the ordered nn samples, we can establish other laws for the degree-distribution of the graph. The phenomena of small world is also discussed.

Keywords

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

R2 v1 2026-06-22T00:13:29.449Z