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2012 Bounds for the annealed return probability on large finite percolation graphs
Florian Sobieczky
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Electron. J. Probab. 17: 1-17 (2012). DOI: 10.1214/EJP.v17-2329


Bounds for the expected return probability of the delayed random walk on finite clusters of an invariant percolation on transitive unimodular graphs are derived. They are particularly suited for the case of critical Bernoulli percolation and the associated heavy-tailed cluster size distributions. The upper bound relies on the fact that cartesian products of finite graphs with cycles of a certain minimal size are Hamiltonian. For critical Bernoulli bond percolation on the homogeneous tree this bound is sharp. The asymptotic type of the expected return probability for large times $t$ in this case is of order $t^{-3/4}$.


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Florian Sobieczky. "Bounds for the annealed return probability on large finite percolation graphs." Electron. J. Probab. 17 1 - 17, 2012.


Accepted: 21 September 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1260.05149
MathSciNet: MR2981904
Digital Object Identifier: 10.1214/EJP.v17-2329

Primary: 47B80
Secondary: 05C81 , 60J27 , 60K35

Keywords: Annealed Return Probability , Anomalous diffusion , Critical Invariant Percolation , Integrated Density of States , Number of open clusters per vertex , Random walks


Vol.17 • 2012
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