Heavy-tailed Distributions In Stochastic Dynamical Models

TL;DR

This paper reviews various stochastic dynamical models that produce heavy-tailed distributions, highlighting their mechanisms and the conditions under which these distributions emerge in complex systems.

Contribution

It provides a comprehensive overview of models leading to heavy-tailed distributions, emphasizing the role of coupling rules and system dynamics.

Findings

Heavy-tailed distributions arise as emergent phenomena in diverse models.

Multiple mechanisms, including multiplicative noise and self-organized criticality, lead to heavy tails.

Heavy tails are sensitive to the coupling rules in the models.

Abstract

Heavy-tailed distributions are found throughout many naturally occurring phenomena. We have reviewed the models of stochastic dynamics that lead to heavy-tailed distributions (and power law distributions, in particular) including the multiplicative noise models, the models subjected to the Degree-Mass-Action principle (the generalized preferential attachment principle), the intermittent behavior occurring in complex physical systems near a bifurcation point, queuing systems, and the models of Self-organized criticality. Heavy-tailed distributions appear in them as the emergent phenomena sensitive for coupling rules essential for the entire dynamics.