Universality for directed polymers in thin rectangles

Abstract

We consider the fluctuations of the free energy of positive temperature directed polymers in thin rectangles (N,N^α), α< 3/14. For general weight distributions with finite fourth moment we prove that the distribution of these fluctuations converges as N goes to infinity to the GUE Tracy-Widom distribution.

12 pages

References in corpus (4)

• Level-Spacing Distributions and the Airy Kernel
• Scaling for a one-dimensional directed polymer with boundary conditions
• A simple invariance theorem
• On the free energy of a directed polymer in a Brownian environment

Cited by in corpus (5)

• Log-Gamma polymer free energy fluctuations via a Fredholm determinant identity
• Fluctuations of the log-gamma polymer free energy with general parameters and slopes
• Tracy-Widom asymptotics for a river delta model
• The scaling relation chi = 2 xi - 1 for directed polymers in a random environment
• Analytical Methods and Field Theory for Disordered Systems