  We express all correlation functions in timelike boundary Liouville theory as
unitary matrix integrals and develop efficient techniques to evaluate these
integrals. We compute large classes of correlation functions explicitly,
including an infinite number of terms in the boundary state of the rolling
tachyon. The matrix integrals arising here also determine the correlation
functions of gauge invariant operators in two dimensional Yang-Mills theory,
suggesting an equivalence between the rolling tachyon and QCD_2.
