The Universal Relation Between Exponents in First-Passage Percolation

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. I will give a rigorous proof of this conjecture assuming that the exponents exist in a certain sense.