How to simulate the quasi-stationary state

TL;DR

This paper introduces an efficient simulation method for studying the quasi-stationary state in processes with absorbing states, demonstrated on the contact process, significantly improving simulation efficiency at criticality.

Contribution

A novel simulation approach based on the QS distribution's equation of motion, enhancing efficiency over traditional methods for analyzing quasi-stationary states.

Findings

Method is about ten times more efficient at the critical point.

Successfully applied to the contact process.

Provides a practical tool for studying absorbing state processes.

Abstract

For a large class of processes with an absorbing state, statistical properties of the surviving sample attain time-independent values in the quasi-stationary (QS) regime. We propose a practical simulation method for studying quasi-stationary properties, based on the equation of motion governing the QS distribution. The method is tested in applications to the contact process. At the critical point, our method is about an order of magnitude more efficient than conventional simulation.