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