Power law in random multiplicative processes with spatio-temporal correlated multipliers

TL;DR

This paper investigates how spatio-temporal correlations in multipliers affect the power-law exponents in random multiplicative processes, revealing different impacts from local and global environmental correlations.

Contribution

It introduces models analyzing the distinct effects of local and global spatio-temporal correlations on power-law exponents in multiplicative processes.

Findings

Local and global environments influence the power-law exponent differently.

Analytical and numerical models demonstrate the distinct trends caused by correlations.

Spatio-temporal correlations can significantly alter the distribution tails.

Abstract

It is well known that random multiplicative processes generate power-law probability distributions. We study how the spatio-temporal correlation of the multipliers influences the power-law exponent. We investigate two sources of the time correlation: the local environment and the global environment. In addition, we introduce two simple models through which we analytically and numerically show that the local and global environments yield different trends in the power-law exponent.