Quasistationary Distribution for the Invasion Model on a Complete Bipartite Graph

TL;DR

This paper analyzes the quasistationary distribution of the Invasion Model on a complete bipartite graph, revealing its limit as one partition grows large and highlighting the model's unique two-time-scale dynamics.

Contribution

It identifies the limit of the quasistationary distribution for the invasion model on bipartite graphs as one partition size tends to infinity, contrasting with related voter model results.

Findings

Limit of quasistationary distribution is highly dispersed

Model exhibits two interacting time scales

Results contrast with voter model behavior

Abstract

The Invasion Model on the complete bibartitle graph was introduced and studied by physicists as a rudimentary model for opinion dynamics on complex networks. We identify the limit of the Quasistationary distribution for the model as one partition size tends to infinity. The limit is a highly dispersed measure. A distinctive feature of the model is that of two time scales with non-trivial interaction. The work and the results complement and are in sharp contrast to the analogous results on the closely related Voter Model.