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We consider a generalization of the Schur process in which a partitionevolves from the empty partition into an arbitrary fixed final partition. Weobtain a double integral representation of the correlation kernel. For aspecial final partition with only one row, the edge scaling limit is alsodiscussed by the use of the saddle point analysis. If we appropriately scalethe length of the row, the limiting correlation kernel changes from theextended Airy kernel.

Correlation function of the Schur process with a fixed final partition