Large deviations for the log-Gamma polymer

TL;DR

This paper derives and proves the lower tail large deviation rate function for the log-Gamma polymer's partition function, connecting it to known results in last passage percolation and Tracy-Widom distribution.

Contribution

It provides an explicit conjecture and rigorous proof for the lower tail large deviation rate function of the log-Gamma polymer, linking it to other models.

Findings

Rate function matches exponential last passage percolation in zero-temperature limit.

Rate function aligns with Tracy-Widom distribution for moderate deviations.

Rigorous proof with one heuristic step remaining.

Abstract

We conjecture an explicit expression for the lower tail large deviation rate function of the partition function of the log-Gamma polymer. We rigorously prove our result, except for one step for which we only provide heuristic evidence. We show that the large deviation rate function matches with that of last passage percolation with exponential weights in the zero-temperature limit, and with the lower tail of the Tracy-Widom distribution for moderate deviations.