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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2144))

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Abstract

Loop measures and their associated loop soups are generally viewed as arising from finite state Markov chains. We generalize several results to loop measures arising from potentially complex edge weights. We discuss two applications: Wilson’s algorithm to produce uniform spanning trees and an isomorphism theorem due to Le Jan.

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Acknowledgements

This research was supported by National Science Foundation grant DMS-0907143.

The authors would like to thank Dapeng Zhan for bringing an error in an earlier version of this paper to our attention.

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Correspondence to Gregory F. Lawler .

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Lawler, G.F., Perlman, J. (2015). Loop Measures and the Gaussian Free Field. In: Biskup, M., Černý, J., Kotecký, R. (eds) Random Walks, Random Fields, and Disordered Systems. Lecture Notes in Mathematics, vol 2144. Springer, Cham. https://doi.org/10.1007/978-3-319-19339-7_5

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