Fluctuation exponents for directed polymers in the intermediate disorder regime

Abstract

We compute the fluctuation exponents for a solvable model of one-dimensional directed polymers in random environment in the intermediate regime. This regime corresponds to taking the inverse temperature to zero with the size of the system. The exponents satisfy the KPZ scaling relation and coincide with physical predictions. In the critical case, we recover the fluctuation exponents of the Cole-Hopf solution of the KPZ equation in equilibrium and close to equilibrium.

30 pages

References in corpus (6)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• A Fredholm Determinant Representation in ASEP
• Log-Gamma polymer free energy fluctuations via a Fredholm determinant identity
• Second class particles and cube root asymptotics for Hammersley's process
• Stochastic integrability and the KPZ equation
• The scaling relation chi = 2 xi - 1 for directed polymers in a random environment

Cited by in corpus (1)

• High temperature limits for $(1+1)$-dimensional directed polymer with heavy-tailed disorder