Open Access
June 2012 Invasion percolation on the Poisson-weighted infinite tree
Louigi Addario-Berry, Simon Griffiths, Ross J. Kang
Ann. Appl. Probab. 22(3): 931-970 (June 2012). DOI: 10.1214/11-AAP761


We study invasion percolation on Aldous’ Poisson-weighted infinite tree, and derive two distinct Markovian representations of the resulting process. One of these is the σ → ∞ limit of a representation discovered by Angel et al. [Ann. Appl. Probab. 36 (2008) 420–466]. We also introduce an exploration process of a randomly weighted Poisson incipient infinite cluster. The dynamics of the new process are much more straightforward to describe than those of invasion percolation, but it turns out that the two processes have extremely similar behavior. Finally, we introduce two new “stationary” representations of the Poisson incipient infinite cluster as random graphs on ℤ which are, in particular, factors of a homogeneous Poisson point process on the upper half-plane ℝ × [0, ∞).


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Louigi Addario-Berry. Simon Griffiths. Ross J. Kang. "Invasion percolation on the Poisson-weighted infinite tree." Ann. Appl. Probab. 22 (3) 931 - 970, June 2012.


Published: June 2012
First available in Project Euclid: 18 May 2012

zbMATH: 1262.60091
MathSciNet: MR2977982
Digital Object Identifier: 10.1214/11-AAP761

Primary: 60C05
Secondary: 60G55

Keywords: Invasion percolation , percolation , Poisson-weighted infinite tree , Prim’s algorithm , Random trees

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.22 • No. 3 • June 2012
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