Distribution in the Geometrically Growing System and Its Evolution

Paper: arXiv 2302.13781

Authors: Kim Chol-jun

Abstract

Recently, we developed a theory of a geometrically growing system. Here we show that the theory can explain some phenomena of power-law distribution including classical demographic and economic and novel pandemic instances, without introduction of delicate economic models but only on the statistical way. A convexity in the low-size part of the distribution is one peculiarity of the theory, which is absent in the power-law distribution. We found that the distribution of the geometrically growing system could have a trend to flatten in the evolution of the system so that the relative ratio of size within the system increases. The system can act as a reverse machine to covert a diffusion in parametric space to a concentration in the size distribution.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides an interesting statistical mechanics approach to power-law distributions and system evolution, showing reasonable mathematical derivations. However, the empirical validation across demographic, economic, and pandemic data lacks rigorous statistical testing and deep backtesting methodology.

Research Flowchart

  flowchart TD
    A[Goal: Explain power-law phenomena & evolution via geometrically growing systems] --> B[Data: Demographic, economic, & pandemic size datasets]
    B --> C[Method: Apply statistical mechanics to geometric growth without economic models]
    C --> D[Process: Map parametric diffusion to size distribution dynamics]
    D --> E[Outcome 1: Identified low-size convexity absent in standard power-laws]
    D --> F[Outcome 2: Distribution flattens over time, concentrating size ratios]