  We develop a Mellin transform framework which allows us to simultaneously
analyze the four known exactly solvable 1+1 dimensional lattice polymer models:
the log-gamma, strict-weak, beta, and inverse-beta models. Using this framework
we prove the conjectured fluctuation exponents of the free energy and the
polymer path for the stationary point-to-point versions of these four models.
The fluctuation exponent for the polymer path was previously unproved for the
strict-weak, beta, and inverse-beta models.
