The universal relation between scaling exponents in first-passage percolation

Abstract

It has been conjectured in numerous physics papers that in ordinary first-passage percolation on integer lattices, the fluctuation exponent $\ddot{I}‡$ and the wandering exponent $\hat{I}¾$ are related through the universal relation $\ddot{I}‡=2\hat{I}¾-1$, 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.

33 pages, 8 figures. To appear in the Annals of Math