Consider two epidemics whose expansions on $mathbb{Z}^d$ are governed by two families of passage times that are distinct and stochastically comparable. We prove that when the weak infection survives, the space occupied by the strong one is almost impossible to detect. Particularly, in dimension two, we prove that one species finally occupies a set with full density, while the other one only occupies a set of null density. Furthermore, we observe the same fluctuations with respect to the asymptotic shape as for the weak infection evolving alone. By the way, we extend the H?ggstr?m-Pemantle non-coexistence result "except perhaps for a denumerable set" to families of stochastically comparable passage times indexed by a continuous parameter.
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机译：考虑两个流行病，它们在$ mathbb {Z} ^ d $上的扩展受两个不同的传代时间家族控制，它们在随机性上是可比的。我们证明，当弱感染得以幸存时，强感染所占据的空间几乎是无法检测到的。特别是，在第二维中，我们证明了一个物种最终占据了全密度集合，而另一物种仅占据了零密度集合。此外，我们观察到关于渐进形状的波动与单独发展的弱感染相同。顺便说一下，我们将H？ggstr？m-Pemantle非共存结果“除了可能为可数集之外”扩展到由连续参数索引的随机可比通过时间的族。
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