Replica Bethe ansatz derivation of the GOE Tracy-Widom distribution in one-dimensional directed polymers with free boundary conditions

Abstract

The distribution function of the free energy fluctuations in one-dimensional directed polymers with free boundary conditions is derived by mapping the replicated problem to the N-particle quantum boson system with attractive interactions. It is shown that in the thermodynamic limit this function is described by the universal Tracy-Widom distribution of the Gaussian orthogonal ensemble.

12 pages, 1 figure

References in corpus (4)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• An exact solution for the KPZ equation with flat initial conditions
• Correlation functions of the one-dimensional attractive Bose gas
• A determinantal formula for the GOE Tracy-Widom distribution

Cited by in corpus (11)

• Spectral theory for the q-Boson particle system
• Interaction quench in a Lieb-Liniger model and the KPZ equation with flat initial conditions
• Two-point free energy distribution function in (1+1) directed polymers
• Half-space stationary Kardar-Parisi-Zhang equation
• Anomalous 1D fluctuations of a simple 2D random walk in a large deviation regime
• Maximum of an Airy process plus Brownian motion and memory in KPZ growth
• $N$-point free energy distribution function in one dimensional random directed polymers
• Brownian flights over a circle
• Log-gamma directed polymer with one free end via coordinate Bethe Ansatz
• Lifshitz tails at spectral edge and holography with a finite cutoff
• Integrability of zero-dimensional replica field theories at beta=1