Zipf's law leads to Heaps' law: analyzing their relation in finite-size systems.

ABSTRACT:

Background

Zipf's law and Heaps' law are observed in disparate complex systems. Of particular interests, these two laws often appear together. Many theoretical models and analyses are performed to understand their co-occurrence in real systems, but it still lacks a clear picture about their relation.

Methodology/principal findings

We show that the Heaps' law can be considered as a derivative phenomenon if the system obeys the Zipf's law. Furthermore, we refine the known approximate solution of the Heaps' exponent provided the Zipf's exponent. We show that the approximate solution is indeed an asymptotic solution for infinite systems, while in the finite-size system the Heaps' exponent is sensitive to the system size. Extensive empirical analysis on tens of disparate systems

SUBMITTER: Lu L 

PROVIDER: S-EPMC2996287 | biostudies-literature | 2010 Dec

REPOSITORIES: biostudies-literature