Timeline for Simple random walk on a locally finite graph: when is it recurrent?
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| Dec 13, 2011 at 22:48 | comment | added | matan.harel | Actually, I'm pretty certain that general binary trees will not be in the class (which is good, because random walks on the uniformly binary tree is transient!). The local weak limit of a binary tree does exist though, and it gives law on the space of rooted infinite trees which is almost like a geometric random variable. Anyway, there is a conjecture in the Benjamini-Schramm paper that being a local weak limit is equivalent to the "intrinsic mass transport" principle - basically the same as a unimodular graph. I think Aldous/Lyons talk about it in arxiv.org/abs/math/0603062 | |
| Dec 13, 2011 at 22:29 | comment | added | David White | +1: Thanks a bunch. I really like this result because it relates to my theorem (universally bounded degree) and because I'm actually a topologist and not a graph theorist. Still, I can't help but ask what types of graphs arise this way. I've only just glanced at the paper and I can see that binary trees, graphs with nice triangulations, and some very cool looking tilings do. If anyone has ideas for other common classes of graphs which this result includes, I'd be interested to hear them! | |
| Dec 13, 2011 at 22:15 | history | answered | matan.harel | CC BY-SA 3.0 |