Multi-colour competition with reinforcement
Channel: Daniel Ahlberg
Date: 2022-05-20

This is a research overview of a paper of Daniel Ahlberg and Carolina Fransson titled "Multi-colour competition with reinforcement". In the paper, we study a system of interacting urns where balls of different colour/type compete for their survival, and annihilate upon contact. For competition between two types, the underlying graph (finite and connected), determining the interaction between the urns, is known to be irrelevant for the possibility of coexistence, whereas for three or more types the structure of the graph does affect the possibility of coexistence. We show that when the underlying graph is a cycle, competition between two or more types almost surely has a single survivor, thus establishing a conjecture of Griffiths, Janson, Morris and the first author. Along the way, we give a detailed description of an auto-annihilative process on the cycle, which can be perceived as an expression of the geometry of a Möbius strip in a discrete setting.

Preprint link: https://arxiv.org/abs/2206.00400
Author webpage: https://staff.math.su.se/daniel.ahlberg/