  In this paper we study two multicritical correlation kernels and prove that
they converge to the Pearcey kernel in a certain double scaling limit. The
first kernel appears in a model of non-intersecting Brownian motions at a
tacnode. The second arises as a triple scaling limit of the eigenvalue
correlation kernel in the Hermitian two-matrix model with quartic/quadratic
potentials. The two kernels are different but can be expressed in terms of the
same tacnode Riemann-Hilbert problem. The proof is based on a steepest descent
analysis of this Riemann-Hilbert problem. A special feature in the analysis is
the introduction of an explicit meromorphic function on a Riemann surface with
specified sheet structure.
