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.
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