  We consider the totally asymmetric simple exclusion process, a model in the
KPZ universality class. We focus on the fluctuations of particle positions
starting with certain deterministic initial conditions. For large time t, one
has regions with constant and linearly decreasing density. The fluctuations on
these two regions are given by the Airy_1 and Airy_2 processes, whose one-point
distributions are the GOE and GUE Tracy-Widom distributions of random matrix
theory. In this paper we analyze the transition region between these two
regimes and obtain the transition process. Its one-point distribution is a new
interpolation between GOE and GUE edge distributions.
