Percolation in 1 + 1 Dimensions at the Uniqueness Threshold
نویسنده
چکیده
For independent density p site percolation on the (transitive non-amenable) graph T b Z, where T b is a homogeneous tree of degree b + 1, and b is supposed to be large, it is shown that for p = p u = inffp: a.s. there is a unique innnite clusterg there are a.s. innnitely many inn-nite clusters. This contrasts with a recent result of Benjamini and Schramm, according to whom for transitive non-amenable planar graphs there is a.s. a unique innnite cluster at p u .
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تاریخ انتشار 2007