Inverting the coupling of the signed Gaussian free field with a loop-soup
Lupu, Titus; Sabot, Christophe; Tarrès, Pierre (2019), Inverting the coupling of the signed Gaussian free field with a loop-soup, Electronic Journal of Probability, 24, p. 1-28. 10.1214/19-EJP326
TypeArticle accepté pour publication ou publié
Journal nameElectronic Journal of Probability
Institute of Mathematical Statistics
MetadataShow full item record
Laboratoire de Probabilités, Statistiques et Modélisations [LPSM (UMR_8001)]
Institut Camille Jordan [Villeurbanne] [ICJ]
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)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.
Subjects / KeywordsGaussian free field; Ising model; loop-soups; random currents; Ray-Knight identity; self-interacting processes
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