The frog model on trees with drift

• DOI: 10.1214/19-ecp235
• Publication Date: 2019-06-01T02:04:40Z
• Authors: Erin Beckman; Natalie Frank; Yufeng Jiang; Matthew Junge; Si Tang
• Keywords: 60J80; recurrence; Probability (math.PR); 01 natural sciences; 60K35; FOS: Mathematics; 60J10; coupling; 0101 mathematics; 60K35, 60J80, 60J10; frog model; interacting particle system; Mathematics - Probability

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