Loop Measures and the Gaussian Free Field

  • Gregory F. LawlerEmail author
  • Jacob Perlman
Part of the Lecture Notes in Mathematics book series (LNM, volume 2144)


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.


Span Tree Continuous Time Markov Chain Path Measure Loop Measure Gamma Random Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



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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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA

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