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Random two-component spanning forests · Around

2012

Random two-component spanning forests

Kassel, Adrien, Kenyon, Richard, Wu, Wei

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We study random two-component spanning forests ($2$SFs) of finite graphs, giving formulas for the first and second moments of the sizes of the components, vertex-inclusion probabilities for one or two vertices, and the probability that an edge separates the components.

We compute the limit of these quantities when the graph tends to an infinite periodic graph in ${\mathbb R}^d$.

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G. Pólya
1948
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P. G. Doyle, J. L. Snell
1984
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W. Myrvold
1992
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R. Burton, R. Pemantle
1993
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