Crossover in the log-gamma polymer from the replica coordinate Bethe Ansatz

Abstract

The coordinate Bethe Ansatz solution of the log-gamma polymer is extended to boundary conditions with one fixed end and the other attached to one half of a one-dimensional lattice. The large-time limit is studied using a saddle-point approximation,and the cumulative distribution function of the rescaled free energy of a long polymer is expressed as a Fredholm determinant. Scaling limits of the kernel are identified, leading to a crossover from the GUE to the GOE Tracy--Widom distributions. The continuum limit reproduces the crossover from droplet to flat initial conditions of the Kardar--Parisi--Zhang equation.

arXiv comment20 pages

References in corpus (25)

• Level-Spacing Distributions and the Airy Kernel
• 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
• Solution for an interaction quench in the Lieb-Liniger Bose gas
• Bethe anzats derivation of the Tracy-Widom distribution for one-dimensional directed polymers
• An exact solution for the KPZ equation with flat initial conditions
• Scaling for a one-dimensional directed polymer with boundary conditions
• Exact solution for the stationary Kardar-Parisi-Zhang equation
• The KPZ equation with flat initial condition and the directed polymer with one free end
• Random-walk in Beta-distributed random environment
• Correlation functions of the one-dimensional attractive Bose gas
• Probability distribution of the free energy of a directed polymer in a random medium
• A determinantal formula for the GOE Tracy-Widom distribution
• Directed polymer near a hard wall and KPZ equation in the half-space
• The One-dimensional KPZ Equation and the Airy Process
• The strict-weak lattice polymer
• 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
• Ground state energy of a non-integer number of particles with delta attractive interactions
• Point-to-line polymers and orthogonal Whittaker functions
• Diffusion in time-dependent random media and the Kardar-Parisi-Zhang equation
• Crossover from droplet to flat initial conditions in the KPZ equation from the replica Bethe ansatz
• Exact solution for a random walk in a time-dependent 1D random environment: the point-to-point Beta polymer
• Log-gamma directed polymer with one free end via coordinate Bethe Ansatz