Academic Journal
From loop clusters and random interlacements to the free field
| العنوان: | From loop clusters and random interlacements to the free field |
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| المؤلفون: | Lupu, Titus |
| المساهمون: | Laboratoire de Mathématiques d'Orsay (LM-Orsay), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS) |
| المصدر: | ISSN: 0091-1798. |
| بيانات النشر: | HAL CCSD Institute of Mathematical Statistics |
| سنة النشر: | 2016 |
| مصطلحات موضوعية: | random interlacements, percolation by loops, Poisson ensemble of Markov loops, loop soup, Gaussian free field, vacant set, metric graph, isomorphism theorems, 60G15, 60G60, 60J27, 60J60, 60J65, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] |
| الوصف: | Author's version, 25 pages, 1 figure. Compared to the version published in AOP, this one contains a detailed argument that was missing in the proof of Proposition 4.2. The bibliography has also been updated and some typos have been corrected. ; International audience ; It was shown by Le Jan that the occupation field of a Poisson ensemble of Markov loops ("loop soup") of parameter one-half associated to a transient symmetric Markov jump process on a network is half the square of the Gaussian free field on this network. We construct a coupling between these loops and the free field such that an additional constraint holds: the sign of the free field is constant on each cluster of loops. As a consequence of our coupling we deduce that the loop clusters of parameter one-half do not percolate on periodic lattices. We also construct a coupling between the random interlacement on $\mathbb{Z}^{d}$, $d\geq 3$, introduced by Sznitman, and the Gaussian free field on the lattice such that the set of vertices visited by the interlacement is contained in a level set of the free field. We deduce an inequality between the critical level for the percolation by level sets of the free field and the critical parameter for the percolation of the vacant set of the random interlacement. |
| نوع الوثيقة: | article in journal/newspaper |
| اللغة: | English |
| Relation: | info:eu-repo/semantics/altIdentifier/arxiv/1402.0298; hal-00940805; https://hal.science/hal-00940805; https://hal.science/hal-00940805v7/document; https://hal.science/hal-00940805v7/file/Loop%20Clusters%20Interlacements%20Sign%20GFF%20Corrected.pdf; ARXIV: 1402.0298 |
| DOI: | 10.1214/15-AOP1019 |
| الاتاحة: | https://hal.science/hal-00940805 https://hal.science/hal-00940805v7/document https://hal.science/hal-00940805v7/file/Loop%20Clusters%20Interlacements%20Sign%20GFF%20Corrected.pdf https://doi.org/10.1214/15-AOP1019 |
| Rights: | info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.B12D0968 |
| قاعدة البيانات: | BASE |
| DOI: | 10.1214/15-AOP1019 |
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