# Carolina Fransson: Multi-colour competition on a cycle

**Time: **
Wed 2022-06-15 15.15 - 16.00

**Location: **
Kräftriket, house 6, room 306

**Participating: **
Carolina Fransson (Stockholm University)

### Abstract

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 to the possibility of coexistence, whereas for *K*>2 types the structure of the graph does affect the possibility of coexistence. We show that when the underlying graph is a cycle, competition between *K*>2 types almost surely has a single survivor, thus establishing a conjecture of Ahlberg, Griffiths, Janson and Morris. Along the way, we establish asymptotic results for 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. This is joint work with D. Ahlberg.