Sensitivity of the frog model to initial conditions
Sensitivity of the frog model to initial conditions
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DOI：
10.1214/19-ecp230
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发表时间：
2018-09
影响因子：
0.5
通讯作者：
Tobias Johnson;L. Rolla
中科院分区：
文献类型：
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作者：
Tobias Johnson;L. Rolla
青蛙模型是图形上相互作用的粒子系统。活动粒子执行独立的简单随机行走，而休眠粒子保持惰性，直到活动粒子访问。在每个独立于特定分布的采样位置放置一定数量的休眠粒子，然后激活一个粒子以开始该过程。我们证明了模型的常返性或暂时性不仅对期望，而且对整个分布都很敏感。这与分支随机行走和激活随机行走等密切相关的模型形成了鲜明对比。
The frog model is an interacting particle system on a graph. Active particles perform independent simple random walks, while sleeping particles remain inert until visited by an active particle. Some number of sleeping particles are placed at each site sampled independently from a certain distribution, and then one particle is activated to begin the process. We show that the recurrence or transience of the model is sensitive not just to the expectation but to the entire distribution. This is in contrast to closely related models like branching random walk and activated random walk.