# Statistical properties of one-dimensional directed polymers in a random potential

## TL;DR

This review explores the universal statistical behaviors of one-dimensional directed polymers in random potentials, deriving exact results for free energy distributions and discussing open problems in the field.

## Contribution

It provides a comprehensive analysis using the replica Bethe ansatz technique and presents new exact results for free energy distribution functions.

## Key findings

- Derived exact free energy distribution functions
- Identified open problems in the statistical properties of directed polymers
- Provided technical details of the replica Bethe ansatz calculations

## Abstract

This review is devoted to the detailed consideration of the universal statistical properties of one-dimensional directed polymers in a random potential. In terms of the replica Bethe ansatz technique we derive several exact results for different types of the free energy probability distribution functions. In the second part of the review we discuss the problems which are still waiting for their solutions. Several mathematical appendices in the ending part of the review contain various technical details of the performed calculations.