Some new results on one-dimensional outflow dynamics

TL;DR

This paper introduces a simplified version of the one-dimensional outflow dynamics model, demonstrating that it matches the original in simulations and deriving an analytical formula for exit probability that aligns with computational results.

Contribution

The paper presents a modified outflow dynamics model that simplifies analysis and provides an analytical formula for exit probability, validated by simulations and comparisons with previous methods.

Findings

Modified model matches original simulation results

Analytical exit probability formula agrees with simulations

Kirkwood approximation is effective beyond expected conditions

Abstract

In this paper we introduce modified version of one-dimensional outflow dynamics (known as a Sznajd model) which simplifies the analytical treatment. We show that simulations results of the original and modified rules are exactly the same for various initial conditions. We obtain the analytical formula for exit probability using Kirkwood approximation and we show that it agrees perfectly with computer simulations in case of random initial conditions. Moreover, we compare our results with earlier analytical calculations obtained from renormalization group and from general sequential probabilistic frame introduced by Galam. Using computer simulations we investigate the time evolution of several correlation functions to show if Kirkwood approximation can be justified. Surprisingly, it occurs that Kirkwood approximation gives correct results even for these initial conditions for which it cannot be easily justified.