- Journal Article
Rights / licenseIn Copyright - Non-Commercial Use Permitted
When a simply connected domain D ⊂ Rd (d ≥ 2) is approximated in a “good” way by embedded connected weighted graphs, we prove that the transfer current matrix (defined on the edges of the graph viewed as an electrical network) converges, up to a local weight factor, to the differential of Green’s function on D. This observation implies that properly rescaled correlations of the spanning tree model and correlations of minimal subconfigurations in the abelian sandpile model have a universal and conformally covariant limit. We further show that, on a periodic approximation of the domain, all pattern fields of the spanning tree model, as well as the minimal-pattern (e.g. zero-height) fields of the sandpile, converge weakly in distribution to Gaussian white noise. Show more
Journal / seriesProbability Theory and Related Fields
Pages / Article No.
SubjectTransfer current theorem; Spanning trees; Sandpiles; Patterns
Organisational unit09453 - Werner, Wendelin / Werner, Wendelin
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Is new version of: http://hdl.handle.net/20.500.11850/78611
NotesIt was possible to publish this article open access thanks to a Swiss National Licence with the publisher.
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