Characterizing stationary 1+1 dimensional lattice polymer models

TL;DR

This paper characterizes a unique integrability property shared by several lattice polymer models, revealing their special distribution-preserving ratios and Burke property, and demonstrating its exclusivity among similar models.

Contribution

It introduces a new integrability property for lattice polymer models and proves its uniqueness among models with certain regularity conditions.

Findings

Identifies a shared integrability property among specific polymer models

Shows the property implies the Burke property in these models

Proves the property is unique to these models under regularity assumptions

Abstract

Motivated by the study of directed polymer models with random weights on the square integer lattice, we define an integrability property shared by the log-gamma, strict-weak, beta, and inverse-beta models. This integrability property encapsulates a preservation in distribution of ratios of partition functions which in turn implies the so called Burke property. We show that under some regularity assumptions, up to trivial modifications, there exist no other models possessing this property.