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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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 $\xi$ 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).

Article information

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

Dates
First available in Project Euclid: 26 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.aop/1395838127

Digital Object Identifier
doi:10.1214/13-AOP854

Mathematical Reviews number (MathSciNet)
MR3189069

Zentralblatt MATH identifier
1296.60257

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

Keywords
First-passage percolation KPZ relation

Citation

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. https://projecteuclid.org/euclid.aop/1395838127


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