The frog model on trees with drift

Electronic Communications in Probability

Erin Beckman¹ 

关键词: frog model;    interacting particle system;    coupling;    recurrence;   

DOI  :  10.1214/19-ECP235

学科分类：统计和概率

来源: Institute of Mathematical Statistics

【 摘 要 】

We provide a uniform upper bound on the minimal drift so that the one-per-site frog model on a $d$-ary tree is recurrent. To do this, we introduce a subprocess that couples across trees with different degrees. Finding couplings for frog models on nested sequences of graphs is known to be difficult. The upper bound comes from combining the coupling with a new, simpler proof that the frog model on a binary tree is recurrent when the drift is sufficiently strong. Additionally, we describe a coupling between frog models on trees for which the degree of the smaller tree divides that of the larger one. This implies that the critical drift has a limit as $d$ tends to infinity along certain subsequences.

【 授权许可】

CC BY