Quasi-stationary simulation of the contact process

TL;DR

This paper reviews a Monte Carlo simulation method for studying quasi-stationary states in stochastic processes with absorbing states, applying it to the critical contact process to analyze correlation functions and interparticle distributions.

Contribution

It introduces and applies a novel Monte Carlo simulation technique for quasi-stationary analysis of processes with absorbing states, specifically in the contact process.

Findings

Determined static correlation functions in the critical contact process.

Analyzed interparticle gap-length distribution and found power-law decay.

Provided evidence for power-law decay in two-particle subspace.

Abstract

We review a recently devised Monte Carlo simulation method for the direct study of quasi-stationary properties of stochastic processes with an absorbing state. The method is used to determine the static correlation function and the interparticle gap-length distribution in the critical one-dimensional contact process. We also find evidence for power-law decay of the interparticle distance distribution in the two-particle subspace.