Transience, Recurrence and Critical Behavior for Long-Range Percolation

Details Transience, Recurrence and Critical Behavior for Long-Range Percolation Transience, Recurrence and Critical Behavior for Long-Range Percolation

2001-10-26

arxiv.org/abs/math/0110296v2

Mathematics

Probability

36 pages Minor changes, this is the journal version

Scientific paper

10.1007/s002200200617

We study the behavior of the random walk on the infinite cluster of independent long range percolation in dimensions $d=1,2$, where $x$ and $y$ a re connected with probability $\sim\beta/\|x-y\|^{-s}$. We show that when $d

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