Unidirectional Random Growth with Resetting

TL;DR

This paper reviews stochastic processes without detailed balance, analyzing their stationary distributions and stability, and introduces a simple model with resetting applied to diverse real-world systems.

Contribution

It classifies non-detailed balance stochastic processes, derives their stationary distributions, and applies a simple growth-resetting model to various complex systems.

Findings

Stationary distributions characterized beyond Kullback-Leibler divergence

Model explains diverse phenomena like network popularity and income distribution

Stability analysis of non-equilibrium stochastic processes

Abstract

We review and classify stochastic processes without detailed balance condition. We obtain stationary distributions and investigate their stability in terms of generalized entropic divergences beyond the Kullback-Leibler formula. A simple stochastic model with local growth rates and direct resetting to the ground state is investigated and applied to various networks, scientific citations and Facebook popularity, hadronic yields in high energy particle reactions, income and wealth distributions, biodiversity and settlement size distribution.