On a geometric mean and power-law statistical distributions

TL;DR

This paper explores the relationship between geometric means and power-law distributions in statistical systems, revealing constraints on observable quantities.

Contribution

It introduces a framework linking geometric means to power-law distributions, providing new insights into their constraints in statistical systems.

Findings

Geometric means are constrained in systems with power-law distributions.

Power-law distributions characterize a wide class of statistical observables.

The framework offers a new perspective on statistical constraints.

Abstract

For a large class of statistical systems a geometric mean value of the observables is constrained. These observables are characterized by a power-law statistical distribution.