The Annals of Probability

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

Antonio Auffinger and Michael Damron

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In a recent breakthrough work, Chatterjee [Ann. of Math. (2) 177 (2013) 663–697] proved a long standing conjecture that relates the transversal exponent $\xi$ and the fluctuation exponent $\chi$ in first-passage percolation on $\mathbb{Z}^{d}$. 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 $\chi\leq2\xi-1$. One advantage of our argument is that it does not require the “nearly Gamma” assumption of Chatterjee (2013).

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Ann. Probab., Volume 42, Number 3 (2014), 1197-1211.

First available in Project Euclid: 26 March 2014

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82B43: Percolation [See also 60K35]

First-passage percolation KPZ relation


Auffinger, Antonio; Damron, Michael. A simplified proof of the relation between scaling exponents in first-passage percolation. Ann. Probab. 42 (2014), no. 3, 1197--1211. doi:10.1214/13-AOP854.

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