  We introduce a general model of dimer coverings of certain plane bipartite
graphs, which we call rail yard graphs (RYG). The transfer matrices used to
compute the partition function are shown to be isomorphic to certain operators
arising in the so-called boson-fermion correspondence. This allows to
reformulate the RYG dimer model as a Schur process, i.e. as a random sequence
of integer partitions subject to some interlacing conditions.
  Beyond the computation of the partition function, we provide an explicit
expression for all correlation functions or, equivalently, for the inverse
Kasteleyn matrix of the RYG dimer model. This expression, which is amenable to
asymptotic analysis, follows from an exact combinatorial description of the
operators localizing dimers in the transfer-matrix formalism, and then a
suitable application of Wick's theorem.
  Plane partitions, domino tilings of the Aztec diamond, pyramid partitions,
and steep tilings arise as particular cases of the RYG dimer model. For the
Aztec diamond, we provide new derivations of the edge-probability generating
function, of the biased creation rate, of the inverse Kasteleyn matrix and of
the arctic circle theorem.
