  In this paper, we study the bead model: beads are threaded on a set of wires
on the plane represented by parallel straight lines. We add the constraint that
between two consecutive beads on a wire; there must be exactly one bead on each
neighboring wire. We construct a one-parameter family of Gibbs measures on the
bead configurations that are uniform in a certain sense. When endowed with one
of these measures, this model is shown to be a determinantal point process,
whose marginal on each wire is the sine process (given by eigenvalues of large
hermitian random matrices). We prove then that this process appears as a limit
of any dimer model on a planar bipartite graph when some weights degenerate.
