OxTalks will soon move to the new Halo platform and will become 'Oxford Events.' There will be a need for an OxTalks freeze. This was previously planned for Friday 14th November – a new date will be shared as soon as it is available (full details will be available on the Staff Gateway).
In the meantime, the OxTalks site will remain active and events will continue to be published.
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We study a system of interacting urns where balls of different colour/type compete for their survival, and annihilate upon contact. We shall consider the finite setting, i.e. when the underlying graph is finite and connected. In this case it is known that coexistence is not possible between two types. However, for competition between three or more types, the possibility of coexistence depends on the underlying graph. We prove a conjecture stating that when the underlying graph is a cycle, then the competition between three or more types has a single survivor almost surely. As part of the proof 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. (Joint work with Carolina Fransson.)
