Open Access
2019 Invasion percolation on Galton-Watson trees
Marcus Michelen, Robin Pemantle, Josh Rosenberg
Electron. J. Probab. 24: 1-35 (2019). DOI: 10.1214/19-EJP281


We consider invasion percolation on Galton-Watson trees. On almost every Galton-Watson tree, the invasion cluster almost surely contains only one infinite path. This means that for almost every Galton-Watson tree, invasion percolation induces a probability measure on infinite paths from the root. We show that under certain conditions of the progeny distribution, this measure is absolutely continuous with respect to the limit uniform measure. This confirms that invasion percolation, an efficient self-tuning algorithm, may be used to sample approximately from the limit uniform distribution. Additionally, we analyze the forward maximal weights along the backbone of the invasion cluster and prove a limit law for the process.


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Marcus Michelen. Robin Pemantle. Josh Rosenberg. "Invasion percolation on Galton-Watson trees." Electron. J. Probab. 24 1 - 35, 2019.


Received: 28 March 2018; Accepted: 18 February 2019; Published: 2019
First available in Project Euclid: 3 April 2019

zbMATH: 07055669
MathSciNet: MR3940761
Digital Object Identifier: 10.1214/19-EJP281

Primary: 60K35

Keywords: backbone , Incipient infinite cluster , limit uniform , pivot , Poisson point process , Self-organized criticality

Vol.24 • 2019
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