A simple study of the correlation effects in the superposition of waves of electric fields: the emergence of extreme events

TL;DR

This paper investigates how correlated random phases in superimposed electric waves lead to heavier tail distributions and the emergence of extreme events, highlighting a simple method applicable to nonlinear complex systems.

Contribution

It demonstrates that correlated phase randomness causes extreme events in wave superpositions, providing a straightforward approach to study such phenomena in complex systems.

Findings

Heavier tail distributions observed with increased phase correlation

Extreme events emerge as phase correlation increases

Method applicable to various nonlinear complex systems

Abstract

In this paper, we study the effects of correlated random phases in the intensity of a superposition of $N$ wave-fields. Our results suggest that regardless of whether the phase distribution is continuous or discrete if the phases are random correlated variables, we must observe a heavier tail distribution and the emergence of extreme events as the correlation between phases increases. We believe that such a simple method can be easily applied in other situations to show the existence of extreme statistical events in the context of nonlinear complex systems.