An Identity in Distribution Between Full-Space and Half-Space Log-Gamma Polymers

Abstract We prove an identity in distribution between two kinds of partition functions for the log-gamma directed polymer model: (1) point-to-point function a quadrant and (2) point-to-line octant. As application, we that free energy octant obeys phase transition depending on strength noise along boundary. This (de)pinning by randomness was first predicted physics Kardar 1985 proved rigorously zero temperature models Baik Rains 2001. While it is expected to arise universally Kardar–Parisi–Zhang universality class, this positive model which can be established.