Scaling limit of the invasion percolation cluster on a regular tree
Résumé
We prove existence of the scaling limit of the invasion percolation cluster (IPC) on a regular tree. The limit is a random real tree with a single end. The contour and height functions of the limit are described as certain diffusive stochastic processes.
This convergence allows us to recover and make precise certain asymptotic results for the MC. In particular, we relate the limit of the rescaled level sets of the MC to the local time of the scaled height function.