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Scaling limit of the invasion percolation cluster on a regular tree. (English) Zbl 1281.60076

The authors study the invasion percolation cluster as a metric space with respect to graph distance. They prove that the rescale rooted incipient infinite cluster has a scaling limit w.r.t. the pointed Gramov-Hausdorff topology. The limit is a random real tree and its contour and height functions are described as certain diffusive processes. Using this convergence, the authors make precise certain asymptotic results for the invasion percolation cluster.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B43 Percolation

References:

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