Scaling limit of critical percolation clusters on hyperbolic random half-planar triangulations and the associated random walks

Eleanor Archer; David A. Croydon

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arXiv · 2311.11993

Scaling limit of critical percolation clusters on hyperbolic random half-planar triangulations and the associated random walks

Eleanor Archer·David A. Croydon

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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.

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Eleanor Archer, David A. Croydon. 2023-11-20. Scaling limit of critical percolation clusters on hyperbolic random half-planar triangulations and the associated random walks. https://arxiv.org/abs/2311.11993

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