A simplified proof of the relation between scaling exponents in first-passage percolation

Antonio Auffinger, Michael Damron

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

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).

Original languageEnglish (US)
Pages (from-to)1197-1211
Number of pages15
JournalAnnals of Probability
Volume42
Issue number3
DOIs
StatePublished - 2014

Keywords

  • First-passage percolation
  • Kpz relation

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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