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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. Thecontour and height functions of the limit are described as certain diffusivestochastic processes. This convergence allows us to recover and make precisecertain asymptotic results for the IPC. In particular, we relate the limit ofthe rescaled level sets of the IPC to the local time of the scaled heightfunction.

Scaling limit of the invasion percolation cluster on a regular tree