Cube root fluctuations for the corner growth model associated to the exclusion process
Abstract
We study the lastpassage 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 lastpassage 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 lastpassage 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 March 2006
 arXiv:
 arXiv:math/0603306
 Bibcode:
 2006math......3306B
 Keywords:

 Mathematics  Probability;
 Mathematical Physics;
 60K35 (Primary);
 82C43 (Secondary)
 EPrint:
 41 pages, 4 figures