Electronic Journal of Probability

Cube Root Fluctuations for the Corner Growth Model Associated to the Exclusion Process

Marton Balazs, Eric Cator, and Timo Seppalainen

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We study the last-passage growth model on the planar integer lattice with exponential weights. With boundary conditions that represent the equilibrium exclusion process as seen from a particle right after its jump we prove that the variance of the last-passage time in a characteristic direction is of order $t^{2/3}$. With more general boundary conditions that include the rarefaction fan case we show that the last-passage time fluctuations are still of order $t^{1/3}$, and also that the transversal fluctuations of the maximal path have order $t^{2/3}$. We adapt and then build on a recent study of Hammersley's process by Cator and Groeneboom, and also utilize the competition interface introduced by Ferrari, Martin and Pimentel. The arguments are entirely probabilistic, and no use is made of the combinatorics of Young tableaux or methods of asymptotic analysis.

Article information

Electron. J. Probab., Volume 11 (2006), paper no. 42, 1094-1132.

Accepted: 29 November 2006
First available in Project Euclid: 31 May 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Last-passage simple exclusion cube root asymptotics competition interface Burke's theorem rarefaction fan

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Balazs, Marton; Cator, Eric; Seppalainen, Timo. Cube Root Fluctuations for the Corner Growth Model Associated to the Exclusion Process. Electron. J. Probab. 11 (2006), paper no. 42, 1094--1132. doi:10.1214/EJP.v11-366. https://projecteuclid.org/euclid.ejp/1464730577

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