Loop Measures and the Gaussian Free Field
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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.
KeywordsSpan Tree Continuous Time Markov Chain Path Measure Loop Measure Gamma Random Variable
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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