On the chemical distance for supercritical Bernoulli percolation
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Publication:2563949
DOI10.1214/aop/1039639377zbMath0871.60089OpenAlexW1986564122MaRDI QIDQ2563949
Publication date: 24 September 1997
Published in: The Annals of Probability (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1214/aop/1039639377
percolationlarge deviationsgraph distanceBernoulli bond percolationsupercritical phaserenormalization techniques
Interacting random processes; statistical mechanics type models; percolation theory (60K35) Percolation (82B43)
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Cites Work
- Unnamed Item
- Parabolic problems for the Anderson model. I: Intermittency and related topics
- First passage percolation for random colorings of \(\mathbb{Z}^ d\)
- Sharpness of the phase transition in percolation models
- Surface order large deviations for Ising, Potts and percolation models
- Surface order large deviations for high-density percolation
- The supercritical phase of percolation is well behaved
- Large deviations for discrete and continuous percolation
- Darcy equation for random porous media