Cube root fluctuations for the corner growth model associated to the exclusion process

M. Balázs*, E. Cator, T. Seppäläinen

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

40 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1094-1132
Number of pages39
JournalElectronic Journal of Probability
Volume11
DOIs
Publication statusPublished - 2006

Keywords

  • Burke's theorem
  • Competition interface
  • Cube root asymptotics
  • Last-passage
  • Rarefaction fan
  • Simple exclusion

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