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January 2013 Scaling limit of the invasion percolation cluster on a regular tree
Omer Angel, Jesse Goodman, Mathieu Merle
Ann. Probab. 41(1): 229-261 (January 2013). DOI: 10.1214/11-AOP731

Abstract

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.

Citation

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Omer Angel. Jesse Goodman. Mathieu Merle. "Scaling limit of the invasion percolation cluster on a regular tree." Ann. Probab. 41 (1) 229 - 261, January 2013. https://doi.org/10.1214/11-AOP731

Information

Published: January 2013
First available in Project Euclid: 23 January 2013

zbMATH: 1281.60076
MathSciNet: MR3059198
Digital Object Identifier: 10.1214/11-AOP731

Subjects:
Primary: 60K35 , 82B43

Keywords: Invasion percolation , real tree , Scaling limit

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.41 • No. 1 • January 2013
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