$N$-point free energy distribution function in one dimensional random directed polymers

TL;DR

This paper derives an explicit formula for the joint distribution of free energies at multiple points in a one-dimensional directed polymer model using the Bethe ansatz replica method, confirming previous results.

Contribution

It provides a new derivation of the N-point free energy distribution function in directed polymers, using the Bethe ansatz replica technique, aligning with earlier findings.

Findings

Explicit N-point free energy distribution formula derived

Method confirms previous results by Prolhac and Spohn

Advances analytical understanding of directed polymers in random media

Abstract

Explicit expression for the $N$-point free energy distribution function in one dimensional directed polymers in a random potential is derived in terms of the Bethe ansatz replica technique. The obtained result is equivalent to the one derived earlier by Prolhac and Spohn [J. Stat. Mech., 2011, P03020].