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May 2014 A simplified proof of the relation between scaling exponents in first-passage percolation
Antonio Auffinger, Michael Damron
Ann. Probab. 42(3): 1197-1211 (May 2014). DOI: 10.1214/13-AOP854

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).

Citation

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Antonio Auffinger. Michael Damron. "A simplified proof of the relation between scaling exponents in first-passage percolation." Ann. Probab. 42 (3) 1197 - 1211, May 2014. https://doi.org/10.1214/13-AOP854

Information

Published: May 2014
First available in Project Euclid: 26 March 2014

zbMATH: 1296.60257
MathSciNet: MR3189069
Digital Object Identifier: 10.1214/13-AOP854

Subjects:
Primary: 60K35, 82B43

Rights: Copyright © 2014 Institute of Mathematical Statistics

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Vol.42 • No. 3 • May 2014
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