Scaling limit of critical percolation clusters on hyperbolic random half-planar triangulations and the associated random walks
Probability
2023-11-21 v1
Abstract
We show that the Gromov-Hausdorff-Prohorov scaling limit of a critical percolation cluster on a random hyperbolic triangulation of the half-plane is the Brownian continuum random tree. As a corollary, we obtain that a simple random walk on the critical cluster rescales to Brownian motion on the continuum random tree.
Keywords
Cite
@article{arxiv.2311.11993,
title = {Scaling limit of critical percolation clusters on hyperbolic random half-planar triangulations and the associated random walks},
author = {Eleanor Archer and David A. Croydon},
journal= {arXiv preprint arXiv:2311.11993},
year = {2023}
}
Comments
53 pages