Loop Correlations in Random Wire Models

@article{Benassi2019LoopCI,
  title={Loop Correlations in Random Wire Models},
  author={Costanza Benassi and Daniel Ueltschi},
  journal={Communications in Mathematical Physics},
  year={2019},
  volume={374},
  pages={525-547}
}
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. 
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  • L. Taggi
  • Mathematics
    Communications on Pure and Applied Mathematics
  • 2021
Our first main result is that correlations between monomers in the dimer model in ℤd do not decay to 0 when d>2 . This is the first rigorous result about correlations in the dimer model in dimensions
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