Scaling limit of the invasion percolation cluster on a regular tree

Details Scaling limit of the invasion percolation cluster on a regular tree Scaling limit of the invasion percolation cluster on a regular tree

2009-10-22

arxiv.org/abs/0910.4205v1

Mathematics

Probability

37 pages, 1 figure

Scientific paper

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 IPC. In particular, we relate the limit of the rescaled level sets of the IPC to the local time of the scaled height function.

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