Power-law tail distributions and nonergodicity

TL;DR

This paper explores how systems with power-law tail distributions exhibit ergodicity breaking, linking the divergence of moments to nonergodic behavior, thus providing a theoretical framework for understanding such phenomena.

Contribution

It establishes a direct connection between ergodicity breaking and the divergence of moments in power-law distributions, offering new insights into nonergodic systems.

Findings

Power-law tail distributions can cause ergodicity breaking.

Divergence of moments correlates with nonergodic behavior.

Provides a theoretical basis for analyzing nonergodic systems.

Abstract

We establish an explicit correspondence between ergodicity breaking in a system described by power-law tail distributions and the divergence of the moments of these distributions.