TY - JOUR
T1 - Loop Correlations in Random Wire Models
AU - Benassi, Costanza
AU - Ueltschi, Daniel
N1 - Funding Information:
We are grateful to Jakob Bj?rnberg, J?rg Fr?hlich, Peter M?rters, Charles-?douard Pfister, Vedran Sohinger, Akinori Tanaka, and Yvan Velenik, for useful discussions. We thank the referee for valuable comments. CB is supported by the Leverhulme Trust Research Project Grant RPG-2017-228.
Publisher Copyright:
© 2019, The Author(s).
PY - 2020/3/8
Y1 - 2020/3/8
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/85067300845
U2 - 10.1007/s00220-019-03474-9
DO - 10.1007/s00220-019-03474-9
M3 - Article
SN - 0010-3616
VL - 374
SP - 525
EP - 547
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 2
ER -