Range-Renewal Processes: SLLN, Power Law and Beyonds

Abstract

Given $n$ samples of a regular discrete distribution $\pi$, we prove in this article first a serial of SLLNs results (of Dvoretzky and Erdös' type) which implies a typical power law when $\pi$ is heavy-tailed. Constructing a (random) graph from the ordered $n$ samples, we can establish other laws for the degree-distribution of the graph. The phenomena of small world is also discussed.

28 pages

Cited by in corpus (3)

• Range-Renewal Structure in Continued Fractions
• Range-Renewal Structure of I.I.D. Samplings
• Range-Renewal Speed and Entropy for I.I.D Models