  We study semiclassical correlation functions in Liouville field theory on a
two-sphere when all operators have large conformal dimensions. In the usual
approach, such computation involves solving the classical Liouville equation,
which is known to be extremely difficult for higher-point functions. To
overcome this difficulty, we propose a new method based on the Riemann-Hilbert
analysis, which is applied recently to the holographic calculation of
correlation functions in AdS/CFT. The method allows us to directly compute the
correlation functions without solving the Liouville equation explicitly. To
demonstrate its utility, we apply it to three-point functions, which are known
to be solvable, and confirm that it correctly reproduces the classical limit of
the DOZZ formula for quantum three-point functions. This provides good evidence
for the validity of this method.
