# Two-type annihilating systems on the complete and star graph

## TL;DR

This paper investigates the dynamics of two-type annihilating particle systems on complete and star graphs, analyzing extinction times and the impact of asymmetric speeds, extending understanding beyond single-type models.

## Contribution

It introduces a comparative analysis of two-type annihilating systems on specific graph structures and explores the effects of asymmetric particle speeds.

## Key findings

- Extinction times are characterized for two-type systems on complete and star graphs.
- Asymmetric speeds significantly influence the annihilation dynamics.
- Comparison with one-type systems highlights differences in extinction behavior.

## Abstract

Red and blue particles are placed in equal proportion through-out either the complete or star graph and iteratively sampled to take simple random walk steps. Mutual annihilation occurs when particles with different colors meet. We compare the time it takes to extinguish every particle to the analogous time in the (simple to analyze) one-type setting. Additionally, we study the effect of asymmetric particle speeds.