Z^d上的两种群竞争模型
A two-species competition model on Z^d
摘要：
考虑整数格Z^d上的两类随机竞争模型。该模型描述了两个“物种”沿其边界争夺领土的空间演化。空间的每个位点可以仅包含任一类型的一个代表（也称为粒子）。这两种粒子的传播机制是相同的：每个粒子都独立于其他粒子产生后代，并且只能将它们放置在相邻的未被占据或被相反类型的粒子占据的位置。在第二种情况下，旧粒子被新生粒子杀死。每个粒子的出生率等于可用于扩展的相邻站点的数量。我们要解决的主要问题是这两个物种长期共存的可能性。我们已经证明，如果我们开始的过程中，每种类型的许多代表，然后，在相应的第一次通过渗流模型中的极限集是一致弯曲的假设下，有共存的正概率。
英文摘要：
We consider a two-type stochastic competition model on the integer lattice Z^d. The model describes the space evolution of two ``species'' competing for territory along their boundaries. Each site of the space may contain only one representative (also referred to as a particle) of either type. The spread mechanism for both species is the same: each particle produces offspring independently of other particles and can place them only at the neighboring sites that are either unoccupied, or occupied by particles of the opposite type. In the second case, the old particle is killed by the newborn. The rate of birth for each particle is equal to the number of neighboring sites available for expansion. The main problem we address concerns the possibility of the long-term coexistence of the two species. We have shown that if we start the process with finitely many representatives of each type, then, under the assumption that the limit set in the corresponding first passage percolation model is uniformly curved, there is positive probability of coexistence.
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