Math @ Duke

Publications [#343710] of Erin Beckman
Papers Published
 Beckman, E; Frank, N; Jiang, Y; Junge, M; Tang, S, The frog model on trees with drift,
Electronic Communications in Probability, vol. 24
(January, 2019), Institute of Mathematical Statistics [doi]
(last updated on 2020/04/29)
Abstract: © 2019, Institute of Mathematical Statistics. All rights reserved. We provide a uniform upper bound on the minimal drift so that the onepersite frog model on a dary 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.


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