Percolation on Expanders

  • Itai Benjamini
Part of the Lecture Notes in Mathematics book series (LNM, volume 2100)


This section is devoted to percolation on finite graphs. More precisely we will try to understand percolation on a sequence of finite graphs, whose number of vertices tends to infinity. Detailed proofs of the material appearing in this section and additional extensions can be found at [ABS04].


Long Range Boolean Function Monotone Function Random Graph Detailed Proof 
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  1. [ABS04]
    N. Alon, I. Benjamini, A. Stacey, Percolation on finite graphs and isoperimetric inequalities. Ann. Probab. 32(3A), 1727–1745 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  2. [Bis04]
    M. Biskup, On the scaling of the chemical distance in long-range percolation models. Ann. Probab. 32(4), 2938–2977 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  3. [DS13]
    J. Ding, A. Sly, Distances in critical long range percolation. arXiv preprint arXiv:1303.3995 (2013)Google Scholar
  4. [Gri99]
    G. Grimmett, Percolation. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 321, 2nd edn. (Springer, Berlin, 1999)Google Scholar
  5. [HLW06]
    S. Hoory, N. Linial, A. Wigderson, Expander graphs and their applications. Bull. Am. Math. Soc. (N.S.) 43(4), 439–561 (2006) (electronic)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Itai Benjamini
    • 1
  1. 1.Department of MathematicsThe Weizmann Institute of ScienceRehovotIsrael

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