The scaling relation chi = 2 xi - 1 for directed polymers in a random environment
Probability
2014-02-07 v1
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.
Cite
@article{arxiv.1211.0992,
title = {The scaling relation chi = 2 xi - 1 for directed polymers in a random environment},
author = {Antonio Auffinger and Michael Damron},
journal= {arXiv preprint arXiv:1211.0992},
year = {2014}
}
Comments
27 pages