English

Internal DLA on mated-CRT maps

Probability 2024-02-28 v2 Mathematical Physics Analysis of PDEs math.MP

Abstract

We prove a shape theorem for internal diffusion limited aggregation on mated-CRT maps, a family of random planar maps which approximate Liouville quantum gravity (LQG) surfaces. The limit is an LQG harmonic ball, which we constructed in a companion paper. We also prove an analogous result for the divisible sandpile.

Cite

@article{arxiv.2211.04891,
  title  = {Internal DLA on mated-CRT maps},
  author = {Ahmed Bou-Rabee and Ewain Gwynne},
  journal= {arXiv preprint arXiv:2211.04891},
  year   = {2024}
}

Comments

69 pages, 8 figures; v2 minor corrections

R2 v1 2026-06-28T05:30:57.203Z