In a recent breakthrough work, Chatterjee [Ann. of Math. (2) 177 (2013) 663-697] proved a long standing conjecture that relates the transversal exponent ξ and the fluctuation exponent χ 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 χ ≤ 2ξ -1. One advantage of our argument is that it does not require the "nearly Gamma" assumption of Chatterjee (2013).
- First-passage percolation
- Kpz relation
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty