| Abstract: |
| The frog model is a growing particle system in which particles perform independent random walks on a graph and a new particle is added whenever a new site is discovered. It is often used to model the spread of information over a network. In this work, we study the minimal drift $p_d$ so that the one-per-site frog model on a d-ary tree is recurrent. We prove that $p_d\le 1/3$ for all $d\ge 2$, an optimal universal upper bound for $p_d$. To do this, we compare the frog model with the one-per-site self-similar frog model and couple the later across trees of different degrees and different drift parameters. |
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