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

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].

10 pages, 1 figure

References in corpus (18)

• Level-Spacing Distributions and the Airy Kernel
• Shape Fluctuations and Random Matrices
• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• The one-dimensional KPZ equation: an exact solution and its universality
• Free-energy distribution of the directed polymer at high temperature
• Bethe anzats derivation of the Tracy-Widom distribution for one-dimensional directed polymers
• An exact solution for the KPZ equation with flat initial conditions
• Exact height distributions for the KPZ equation with narrow wedge initial condition
• Scaling Limit for the Space-Time Covariance of the Stationary Totally Asymmetric Simple Exclusion Process
• The KPZ equation with flat initial condition and the directed polymer with one free end
• Correlation functions of the one-dimensional attractive Bose gas
• The crossover regime for the weakly asymmetric simple exclusion process
• Probability distribution of the free energy of a directed polymer in a random medium
• Directed polymer near a hard wall and KPZ equation in the half-space
• The One-dimensional KPZ Equation and the Airy Process
• Two-point free energy distribution function in (1+1) directed polymers
• Universal Randomness
• Replica Bethe ansatz derivation of the GOE Tracy-Widom distribution in one-dimensional directed polymers with free boundary conditions

Cited by in corpus (7)

• Renormalization fixed point of the KPZ universality class
• Exact formulas for random growth with half-flat initial data
• Intermediate disorder directed polymers and the multi-layer extension of the stochastic heat equation
• On two-time distribution functions in (1+1) random directed polymers
• KPZ fluctuations in finite volume
• Two-time distribution functions in the Gaussian model of randomly forced Burgers turbulence
• Two-temperature statistics of free energies in (1+1) directed polymers