文章基本信息

标题：The frog model on trees with drift
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作者：Erin Beckman ; Natalie Frank ; Yufeng Jiang 等
期刊名称：Electronic Communications in Probability
印刷版ISSN：1083-589X
出版年度：2019
卷号：24
DOI：10.1214/19-ECP235
语种：English
出版社：Electronic Communications in Probability
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.