Uniform spanning forests
نویسندگان
چکیده
منابع مشابه
Uniform Spanning Forests
We study uniform spanning forest measures on infinite graphs, which are weak limits of uniform spanning tree measures from finite subgraphs. These limits can be taken with free (FSF) or wired (WSF) boundary conditions. Pemantle (1991) proved that the free and wired spanning forests coincide in Z d and that they give a single tree iff d 6 4. In the present work, we extend Pemantle’s alternative ...
متن کاملCouplings of Uniform Spanning Forests
We prove the existence of an automorphism-invariant coupling for the wired and the free uniform spanning forests on connected graphs with residually amenable automorphism groups. MSC: 60D05, 05C05, 60B99, 20F32.
متن کاملEnds in Uniform Spanning Forests
It has hitherto been known that in a transitive unimodular graph, each tree in the wired spanning forest has only one end a.s. We dispense with the assumptions of transitivity and unimodularity, replacing them with a much broader condition on the isoperimetric profile that requires just slightly more than uniform transience. §
متن کاملEnds in Uniform Spanning Forests 1
It has hitherto been known that in a transitive unimodular graph, each tree in the wired spanning forest has only one end a.s. We dispense with the assumptions of transitivity and unimodularity, replacing them with a much broader condition on the isoperimetric profile that requires just slightly more than uniform transience.
متن کاملUniform spanning forests and the bi-Laplacian Gaussian field
For N = n(log n) 1 4 , on the ball in Z4 with radius N we construct a ±1 spin model coupled with the wired spanning forests. We show that as n→∞ the spin field has bi-Laplacian Gaussian field on R4 as its scaling limit. For d ≥ 5, the model can be defined on Zd directly without the N -cutoff. The same scaling limit result holds. Our proof is based on Wilson’s algorithm and a fine analysis of in...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2001
ISSN: 0091-1798
DOI: 10.1214/aop/1008956321