  We study n-point boundary correlation functions in Timelike Boundary
Liouville theory, relevant for open string multiproduction by a decaying
unstable D-brane. We give an exact result for the one-point function of the
tachyon vertex operator and show that it is consistent with a previously
proposed relation to a conserved charge in string theory. We also discuss when
the one-point amplitude vanishes. Using a straightforward perturbative
expansion, we find an explicit expression for a tachyon n-point amplitude for
all n, however the result is still a toy model. The calculation uses a new
asymptotic approximation for Toeplitz determinants, derived by relating the
system to a Dyson gas at finite temperature.
