Open Access
2006 Cube Root Fluctuations for the Corner Growth Model Associated to the Exclusion Process
Marton Balazs, Eric Cator, Timo Seppalainen
Author Affiliations +
Electron. J. Probab. 11: 1094-1132 (2006). DOI: 10.1214/EJP.v11-366


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.


Download Citation

Marton Balazs. Eric Cator. Timo Seppalainen. "Cube Root Fluctuations for the Corner Growth Model Associated to the Exclusion Process." Electron. J. Probab. 11 1094 - 1132, 2006.


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

zbMATH: 1139.60046
MathSciNet: MR2268539
Digital Object Identifier: 10.1214/EJP.v11-366

Primary: 60K35
Secondary: 82C43

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

Vol.11 • 2006
Back to Top