Spanning forests and the vector bundle Laplacian
نویسندگان
چکیده
منابع مشابه
Uniform 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...
متن کاملUniform 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 ...
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We study minimal spanning forests in infinite graphs, which are weak limits of minimal spanning trees from finite subgraphs corresponding to i.i.d. random labels on the edges. These limits can be taken with free or wired boundary conditions, and are denoted FMSF (free minimal spanning forest) and WMSF (wired minimal spanning forest), respectively. The WMSF is also the union of the trees that ar...
متن کاملSpanning forests and the golden ratio
For a graph G, let fij be the number of spanning rooted forests in which vertex j belongs to a tree rooted at i. In this paper, we show that for a path, the fij’s can be expressed as the products of Fibonacci numbers; for a cycle, they are products of Fibonacci and Lucas numbers. The doubly stochastic graph matrix is the matrix F = (fij)n×n f , where f is the total number of spanning rooted for...
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.
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2011
ISSN: 0091-1798
DOI: 10.1214/10-aop596