Distribution in the geometrically growing system and its evolution

Area of Science:

• Statistical physics
• Complex systems theory
• Mathematical modeling

Background:

• Power-law distributions are prevalent in natural and social phenomena.
• Existing models often require complex, system-specific assumptions.
• A unified statistical approach is needed to explain these distributions.

Purpose of the Study:

• To introduce and validate a novel theory of geometrically growing systems.
• To demonstrate the theory's ability to explain diverse power-law phenomena.
• To identify unique characteristics of this new theoretical framework.

Main Methods:

• Development of a statistical theory based on geometric growth.
• Application of the theory to demographic, economic, and COVID-19 data.
• Analysis of distribution diagrams and size concentration.

Main Results:

• The theory successfully explains power-law distributions without complex models.
• A distinct convexity in the low-size region of the distribution was identified.
• The model shows a trend towards size concentration within the system over time.

Conclusions:

• The geometrically growing system theory provides a parsimonious explanation for power-law distributions.
• The theory offers a unique statistical perspective, highlighting size concentration.
• This framework has broad applicability across various scientific domains.