4 papers · 1 filter
Scaling limit of critical percolation clusters on hyperbolic random half-planar triangulations and the associated random walks
Eleanor Archer, David A. Croydon
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 t…
Parabolic Anderson model on critical Galton-Watson trees in a Pareto environment
Eleanor Archer, Anne Pein
The parabolic Anderson model is the heat equation with some extra spatial randomness. In this paper we consider the parabolic Anderson model with i.i.d. Pareto potential on a criti…
Infinite stable looptrees
Eleanor Archer
We give a construction of an infinite stable looptree, which we denote by , and prove that it arises both as a local limit of the compact stable looptrees o…
Brownian motion on stable looptrees
Eleanor Archer
In this article, we introduce Brownian motion on stable looptrees using resistance techniques. We prove an invariance principle characterising it as the scaling limit of random wal…