Scaling in the Inter-Event Time of Random and Seasonal Systems

TL;DR

This paper demonstrates that power-law inter-event times can emerge from populations of agents with varying or changing rates, supported by analytical and numerical evidence, revealing how different rate distributions influence observed behaviors.

Contribution

It introduces a unified framework showing how power-law inter-event times arise from Poissonian agents with diverse or evolving rates, combining analytical and numerical methods.

Findings

Power-law inter-event times emerge from heterogeneous Poissonian agents.

Changing rates at the individual level can produce similar power-law distributions.

The shape of the rate distribution influences the range and deviations of the observed behavior.

Abstract

Interevent times have been studied across various disciplines in search for correlations. In this paper we show analytical and numerical evidence that at the population level a power-law can be obtained by assuming poissonian agents with different characteristic times, and at the individual level by assuming poissonian agents that change the rates at which they perform an event in a random or deterministic fashion. The range in which we expect to see this behavior and the possible deviations from it are studied by considering the shape of the rate distribution.