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We relate the planar random current representation introduced by Griffiths, Hurst and Sherman to the dimer model. More precisely, we provide a measure-preserving map between double random currents (obtained as the sum of two independent random currents) on a planar graph and dimers on an associated bipartite graph. We also construct a nesting field for the double random current, which, under this map, corresponds to the height function of the dimer model. As applications, we provide anarXiv:1712.02305v2 fatcat:kj56amp6nvg4zbxrli7oplgkpy