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

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