A simplified proof of the relation between scaling exponents in first-passage percolation Antonio Auffinger, Michael Damron

In a recent breakthrough work, Chatterjee [Ann. of Math. (2) 177 (2013) 663.697] proved a long standing conjecture that relates the transversal exponent . and the fluctuation exponent . in first-passage percolation on Zd. The purpose of this paper is to replace the main argument of Chatterjee (2013) and give an alternative proof of this relation. Specifically, we show that under the assumption that exponents defined in Chatterjee (2013) exist, one has the relation ..2..1. One advantage of our argument is that it does not require the .nearly Gamma. assumption of Chatterjee (2013).