Optimal tail estimates for directed last passage site percolation with geometric random variables

Journal Article (Journal Article)

In this paper, we obtain optimal uniform lower tail estimates for the probability distribution of the properly scaled length of the longest up/right path of the last passage site percolation model considered by Johansson in [12]. The estimates are used to prove a lower tail moderate deviation result for the model. The estimates also imply the convergence of moments, and also provide a verification of the universal scaling law relating the longitudinal and the transversal fluctuations of the model.

Full Text

Duke Authors

Cited Authors

  • Baik, J; Deift, P; McLaughlin, K; Miller, P; Zhou, X

Published Date

  • January 1, 2001

Published In

Volume / Issue

  • 5 / 6

Start / End Page

  • 1207 - 1250

Electronic International Standard Serial Number (EISSN)

  • 1095-0753

International Standard Serial Number (ISSN)

  • 1095-0761

Digital Object Identifier (DOI)

  • 10.4310/atmp.2001.v5.n6.a7

Citation Source

  • Scopus