Fluctuation exponents for stationary exactly solvable lattice polymer models via a Mellin transform framework

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. An independent and concurrent work by Balazs et al (2018) also gives the path fluctuation result for the beta model.