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Local characteristics, entropy and limit theorems for spanning trees and domino tilings via transfer-impedances. (English) Zbl 0785.60007
This is a paper about uniform measures on spanning trees and perfect matchings (domino tilings) of infinite periodic \(d\)-dimensional lattices. A method for calculating the finite-dimensional marginals and the entropy of the limiting measure, which involves the Green’s function, is presented. The results extend previous work of the second author [Ann. Probab. 19, No. 4, 1559-1574 (1991; Zbl 0758.60010)].

MSC:
60C05 Combinatorial probability
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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