External diffusion-limited aggregation on a spanning-tree-weighted random planar map

@article{Gwynne2019ExternalDA,
  title={External diffusion-limited aggregation on a spanning-tree-weighted random planar map},
  author={Ewain Gwynne and Joshua Pfeffer},
  journal={arXiv: Probability},
  year={2019}
}
Let $M$ be the infinite spanning-tree-weighted random planar map, which is the local limit of finite random planar maps sampled with probability proportional to the number of spanning trees they admit. We show that a.s. the $M$-graph distance diameter of the external diffusion-limited aggregation (DLA) cluster on $M$ run for $m$ steps is of order $m^{2/d + o_m(1)}$, where $d$ is the metric ball volume growth exponent for $M$ (which was shown to exist by Ding-Gwynne, 2018). By known bounds for… 

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