论文标题
多彩竞争与加固
Multi-colour competition with reinforcement
论文作者
论文摘要
我们研究了一种相互作用的骨灰系统的系统，其中不同颜色/类型的球竞争其生存，并在接触时歼灭。对于两种类型之间的竞争，确定urn之间的相互作用的基础图（有限和连接）对于共存的可能性无关，而对于$ k \ ge3 $，该图的结构确实会影响共存的可能性。我们表明，当底层图是一个周期时，几乎肯定有一个幸存者，$ k \ ge3 $类型之间的竞争，从而建立了格里菲斯，詹森，莫里斯和第一作者的猜想。一路上，我们对周期中的自动通知过程进行了详细的描述，可以将其视为在离散环境中Möbius带的几何形状的表达。
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 $K\ge3$ types the structure of the graph does affect the possibility of coexistence. We show that when the underlying graph is a cycle, competition between $K\ge3$ 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.
