The scaling relation chi = 2 xi - 1 for directed polymers in a random environment

Abstract

We prove the scaling relation chi = 2 xi - 1 between the transversal exponent xi and the fluctuation exponent chi for directed polymers in a random environment in d dimensions. The definition of these exponents is similar to that proposed by S. Chatterjee in first-passage percolation. The proof presented here also establishes the relation in the zero temperature version of the model, known as last-passage percolation.

27 pages

References in corpus (4)

• Log-Gamma polymer free energy fluctuations via a Fredholm determinant identity
• Limiting shape for directed percolation models
• Subgaussian concentration and rates of convergence in directed polymers
• Universality for directed polymers in thin rectangles

Cited by in corpus (2)

• Airy processes and variational problems
• Fluctuation exponents for directed polymers in the intermediate disorder regime