Abstract
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].
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
N. Alon, I. Benjamini, A. Stacey, Percolation on finite graphs and isoperimetric inequalities. Ann. Probab. 32(3A), 1727–1745 (2004)
M. Biskup, On the scaling of the chemical distance in long-range percolation models. Ann. Probab. 32(4), 2938–2977 (2004)
J. Ding, A. Sly, Distances in critical long range percolation. arXiv preprint arXiv:1303.3995 (2013)
G. Grimmett, Percolation. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 321, 2nd edn. (Springer, Berlin, 1999)
S. Hoory, N. Linial, A. Wigderson, Expander graphs and their applications. Bull. Am. Math. Soc. (N.S.) 43(4), 439–561 (2006) (electronic)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Benjamini, I. (2013). Percolation on Expanders. In: Coarse Geometry and Randomness. Lecture Notes in Mathematics(), vol 2100. Springer, Cham. https://doi.org/10.1007/978-3-319-02576-6_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-02576-6_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-02575-9
Online ISBN: 978-3-319-02576-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)