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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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464730577

Digital Object Identifier
doi:10.1214/EJP.v11-366

Mathematical Reviews number (MathSciNet)
MR2268539

Zentralblatt MATH identifier
1139.60046

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

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

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

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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