Large deviation rate functions for the partition function in a log-gamma distributed random potential

TL;DR

This paper derives explicit formulas for the large deviation rate functions of the partition function in a 1+1-dimensional directed lattice model with log-gamma distributed random weights, advancing understanding of tail behaviors in such stochastic systems.

Contribution

It provides the first explicit formulas for the large deviation rate functions in the log-gamma directed polymer model, including regularity results for general distributions.

Findings

Explicit formulas for the large deviation rate functions in the log-gamma case.

Regularity properties of the rate function for general distributions.

Insights into tail behaviors of the partition function in directed lattice paths.

Abstract

We study right tail large deviations of the logarithm of the partition function for directed lattice paths in i.i.d. random potentials. The main purpose is the derivation of explicit formulas for the $1+1$-dimensional exactly solvable case with log-gamma distributed random weights. Along the way we establish some regularity results for this rate function for general distributions in arbitrary dimensions.