  The height fluctuations of the models in the KPZ class are expected to
converge to a universal process. The spatial process at equal time is known to
converge to the Airy process or its variations. However, the temporal process,
or more generally the two-dimensional space-time fluctuation field, is less
well understood. We consider this question for the periodic TASEP (totally
asymmetric simple exclusion process). For a particular initial condition, we
evaluate the multi-time and multi-location distribution explicitly in terms of
a multiple integral involving a Fredholm determinant. We then evaluate the
large time limit in the so-called relaxation time scale.
