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2019 Inverting the coupling of the signed Gaussian free field with a loop-soup
Titus Lupu, Christophe Sabot, Pierre Tarrès
Electron. J. Probab. 24: 1-28 (2019). DOI: 10.1214/19-EJP326


Lupu introduced a coupling between a random walk loop-soup and a Gaussian free field, where the sign of the field is constant on each cluster of loops. This coupling is a signed version of isomorphism theorems relating the square of the GFF to the occupation field of Markovian trajectories. His construction starts with a loop-soup, and by adding additional randomness samples a GFF out of it. In this article we provide the inverse construction: starting from a signed free field and using a self-interacting random walk related to this field, we construct a random walk loop-soup. Our construction relies on the previous work by Sabot and Tarrès, which inverts the coupling from the square of the GFF rather than the signed GFF itself.


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Titus Lupu. Christophe Sabot. Pierre Tarrès. "Inverting the coupling of the signed Gaussian free field with a loop-soup." Electron. J. Probab. 24 1 - 28, 2019.


Received: 29 November 2018; Accepted: 23 May 2019; Published: 2019
First available in Project Euclid: 28 June 2019

zbMATH: 07089008
MathSciNet: MR3978220
Digital Object Identifier: 10.1214/19-EJP326

Primary: 60J27 , 60J55
Secondary: 60K35 , 81T25 , 81T60 , 82B20

Keywords: Gaussian free field , Ising model , loop-soups , random currents , Ray-Knight identity , self-interacting processes


Vol.24 • 2019
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