Sensitivity of the frog model to initial conditions

Electronic Communications in Probability

Tobias Johnson¹ 

关键词: frog model;    recurrence;    transience;    branching random walk;    activated random walk;   

DOI  :  10.1214/19-ECP230

学科分类：统计和概率

来源: Institute of Mathematical Statistics

【 摘 要 】

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.

【 授权许可】

CC BY