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During various travels, I encountered the following page on Wikipedia:

http://en.wikipedia.org/wiki/Folner_sequence

The proof in the "Proof of amenability" section is kind of neat and I'd like to incorporate it into some background material because it's easy to appreciate, but it doesn't appear (at least, as far as I can tell) in the one and only one referenced paper (Folner, 1955). The other books, papers, etc I have all talk in the language of means.

Does somebody have a source for this? Or is it a "made-nice-for-Wikipedia" restatement of some result I failed to appreciate in the paper?

DrJosh9000
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1 Answers1

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I'm certain it appears in Grimmett's book "Percolation". It's absolutely central to an argument by Burton and Keane that if a graph is amenable there can be at most one infinite cluster in independent bond percolation so there should be a reference in there.

Glorfindel
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Tim
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  • Wow, ok. I'd somehow never heard of percolation theory before. This is cool!Anyway, I can see density defined in that Burton & Keane paper, but I can't see it in the book – DrJosh9000 May 17 '13 at 02:40