  We study instanton contribution to the partition function of the one matrix
model in the k-th multicritical region, which corresponds to the (2,2k-1)
minimal model coupled to Liouville theory. The instantons in the one matrix
model are given by local extrema of the effective potential for a matrix
eigenvalue and identified with the ZZ branes in Liouville theory. We show that
the 2-instanton contribution in the partition function is universal as well as
the 1-instanton contribution and that the connected part of the 2-instanton
contribution reproduces the annulus amplitudes between the ZZ branes in
Liouville theory. Our result serves as another nontrivial check on the
correspondence between the instantons in the one matrix model and the ZZ branes
in Liouville theory, and also suggests that the expansion of the partition
function in terms of the instanton numbers are universal and gives
systematically ZZ brane amplitudes in Liouville theory.
