%0 Generic %1 benassi2018correlations %A Benassi, Costanza %A Ueltschi, Daniel %D 2018 %K loop representation %R 10.1007/s00220-019-03474-9 %T Loop correlations in random wire models %U http://arxiv.org/abs/1807.06564 %X We introduce a family of loop soup models on the hypercubic lattice. The models involve links on the edges, and random pairings of the link endpoints on the sites. We conjecture that loop correlations of distant points are given by Poisson-Dirichlet correlations in dimensions three and higher. We prove that, in a specific random wire model that is related to the classical XY spin system, the probability that distant sites form an even partition is given by the Poisson-Dirichlet counterpart.

@misc{benassi2018correlations, abstract = {We introduce a family of loop soup models on the hypercubic lattice. The models involve links on the edges, and random pairings of the link endpoints on the sites. We conjecture that loop correlations of distant points are given by Poisson-Dirichlet correlations in dimensions three and higher. We prove that, in a specific random wire model that is related to the classical XY spin system, the probability that distant sites form an even partition is given by the Poisson-Dirichlet counterpart.}, added-at = {2021-11-08T15:32:08.000+0100}, author = {Benassi, Costanza and Ueltschi, Daniel}, biburl = {https://www.bibsonomy.org/bibtex/2a4970f5891edcba4414aeee81f2c7833/gzhou}, description = {Loop correlations in random wire models}, doi = {10.1007/s00220-019-03474-9}, interhash = {02e2abacd63a60365c17165fce583831}, intrahash = {a4970f5891edcba4414aeee81f2c7833}, keywords = {loop representation}, note = {cite arxiv:1807.06564Comment: 20 pages, 5 figures}, timestamp = {2021-11-08T15:32:08.000+0100}, title = {Loop correlations in random wire models}, url = {http://arxiv.org/abs/1807.06564}, year = 2018 }