  The bead process is the particle system defined on parallel lines, with
underlying measure giving constant weight to all configurations in which
particles on neighbouring lines interlace, and zero weight otherwise. Motivated
by the statistical mechanical model of the tiling of an $abc$-hexagon by three
species of rhombi, a finitized version of the bead process is defined. The
corresponding joint distribution can be realized as an eigenvalue probability
density function for a sequence of random matrices. The finitized bead process
is determinantal, and we give the correlation kernel in terms of Jacobi
polynomials. Two scaling limits are considered: a global limit in which the
spacing between lines goes to zero, and a certain bulk scaling limit. In the
global limit the shape of the support of the particles is determined, while in
the bulk scaling limit the bead process kernel of Boutillier is reclaimed,
after approriate identification of the anisotropy parameter therein.
