English

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

R2 v1 2026-06-21T22:33:13.548Z