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

TL;DR

This paper introduces a Mellin transform framework to analyze four exactly solvable lattice polymer models, proving their fluctuation exponents for free energy and path, including previously unproven cases.

Contribution

The paper develops a unified Mellin transform approach to analyze and prove fluctuation exponents for four stationary lattice polymer models.

Findings

Proved fluctuation exponents for free energy in all four models.

Established fluctuation exponents for the polymer path in three models.

Unified analytical framework applicable to multiple models.

Abstract

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.