Indistinguishability of trees in 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 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 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 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 کاملIndistinguishability of the components of random spanning forests
We prove that the infinite components of the Free Uniform Spanning Forest (FUSF) of a Cayley graph are indistinguishable by any invariant property, given that the forest is different from its wired counterpart. Similar result is obtained for the Free Minimal Spanning Forest (FMSF). We also show that with the above assumptions there can only be 0, 1 or infinitely many components, which solves th...
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ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2016
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-016-0707-3