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 $\chi$ and the wandering exponent $\xi$ are related through the universal relation $\chi=2\xi -1$, 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.