Stationary Log-Gamma Polymer in Half-Space

TL;DR

This paper analyzes the half-space log-gamma polymer model with stationary initial conditions, deriving exact distribution formulas, asymptotic behaviors, and tail bounds for the scaled free energy.

Contribution

It provides the first exact formulas, asymptotic analysis, and exponential tail bounds for the stationary half-space log-gamma polymer model.

Findings

Exact distribution formulas along the diagonal in different phases

Asymptotic behaviors under critical scaling

Exponential upper bounds for tail probabilities

Abstract

We study the half-space log-gamma polymer model with stationary initial conditions. We derive exact formulas for the distribution of the partition function along the diagonal across the entire High density phase and Low density phase. We obtain asymptotics of these distributions under the critical scaling. We also prove the first exponential upper bounds for the upper and lower tail of the scaled free energy for these half-space stationary log-gamma models.