Many complex systems reduce their flexibility over time in the sense that the number of options (possible states) diminishes over time. We show that rank distributions of the visits to these states that emerge from such processes are exact power laws with an exponent -1 (Zipf's law). When noise is added to such processes, meaning that from time to time they can also increase the number of their options, the rank distribution remains a power law, with an exponent that is related to the noise level in a remarkably simple way. Sample-space-reducing processes provide a new route to understand the phenomenon of scaling and provide an alternative to the known mechanisms of self-organized criticality, multiplicative processes, or preferential attachment.
Proceedings of the National Academy of Science
- Pub Date:
- April 2015
- Physics - Physics and Society;
- Condensed Matter - Statistical Mechanics
- 7 pages, 5 figures in Proceedings of the National Academy of Sciences USA (published ahead of print April 13, 2015)