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We show that the Gromov-Hausdorff-Prohorov scaling limit of a criticalpercolation cluster on a random hyperbolic triangulation of the half-plane isthe Brownian continuum random tree. As a corollary, we obtain that a simplerandom walk on the critical cluster rescales to Brownian motion on thecontinuum random tree.

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