  Schur process is a time-dependent analog of the Schur measure on partitions
studied in math.RT/9907127. Our first result is that the correlation functions
of the Schur process are determinants with a kernel that has a nice contour
integral representation in terms of the parameters of the process. This general
result is then applied to a particular specialization of the Schur process,
namely to random 3-dimensional Young diagrams. The local geometry of a large
random 3-dimensional diagram is described in terms of a determinantal point
process on a 2-dimensional lattice with the incomplete beta function kernel
(which generalizes the discrete sine kernel). A brief discussion of the
universality of this answer concludes the paper.
