Interaction Effects on the Size Distribution in a Growth Model

TL;DR

This paper investigates how global interactions influence the skewness of size distributions in a growth model, revealing that interaction sign and strength can either suppress or enhance size growth and skewness.

Contribution

It introduces a model with two types of global interactions and derives analytic expressions for moments, showing how interactions affect skewness.

Findings

Interactions can suppress or enhance size growth.

Skewness increases or decreases depending on interaction sign.

Change in skewness grows with coupling strength.

Abstract

We study, both analytically and numerically, the interaction effects on the skewness of the size distribution of elements in a growth model. We incorporate two types of global interaction into the growth model, and develop analytic expressions for the first few moments from which the skewness of the size distribution is calculated. It is found that depending on the sign of coupling, interactions may suppress or enhance the size growth, which in turn leads to the decrease or increase of the skewness. The amount of change tends to increase with the coupling strength, rather irrespectively of the details of the model.