The universal relation between scaling exponents in first-passage percolation
Probability
2012-08-21 v3 Mathematical Physics
math.MP
Abstract
It has been conjectured in numerous physics papers that in ordinary first-passage percolation on integer lattices, the fluctuation exponent and the wandering exponent are related through the universal relation , irrespective of the dimension. This is sometimes called the KPZ relation between the two exponents. This article gives a rigorous proof of this conjecture assuming that the exponents exist in a certain sense.
Cite
@article{arxiv.1105.4566,
title = {The universal relation between scaling exponents in first-passage percolation},
author = {Sourav Chatterjee},
journal= {arXiv preprint arXiv:1105.4566},
year = {2012}
}
Comments
33 pages, 8 figures. To appear in the Annals of Math