关于Z轴上瞬态青蛙模型的适用范围
On the range of the transient frog model on Z
摘要：
在本文中，我们观察青蛙模型，一个相互作用的随机游动的无限系统，在Z上的一个不对称的基础随机游动。在具有固定青蛙分布的瞬时性假设下，我们构造了模型的长期范围的下界的矩的显式公式，以及它们的渐近极限作为基本的随机游动的漂移为零。我们还提供了条件，在该条件下，下界可以按比例缩放，以概率收敛到退化分布在1的漂移消失。
英文摘要：
In this paper we observe the frog model, an infinite system of interacting random walks, on Z with an asymmetric underlying random walk. Under the assumption of transience with a fixed frog distribution, we construct an explicit formula for the moments of the lower bound of the model's long-run range, as well as their asymptotic limits as the drift of the underlying random walk vanishes. We also provide conditions in which the lower bound can be scaled to converge in probability to the degenerate distribution at 1 as the drift vanishes.
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