  The two-time distribution gives the limiting joint distribution of the
heights at two different times of a local 1D random growth model in the curved
geometry. This distribution has been computed in a specific model but is
expected to be universal in the KPZ universality class. Its marginals are the
GUE Tracy-Widom distribution. In this paper we study two limits of the two-time
distribution. The first, is the limit of long time separation when the quotient
of the two times goes to infinity, and the second, is the short time limit when
the quotient goes to zero.
