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Article Dans Une Revue Electronic Journal of Probability Année : 2019

Inverting the coupling of the signed Gaussian free field with a loop-soup

Résumé

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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Dates et versions

hal-02151579 , version 1 (08-06-2019)

Identifiants

Citer

Titus Lupu, Christophe Sabot, Pierre Tarrès. Inverting the coupling of the signed Gaussian free field with a loop-soup. Electronic Journal of Probability, 2019, 24 (70), pp.1-28. ⟨10.1214/19-EJP326⟩. ⟨hal-02151579⟩
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