### Abstract

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.

Original language | English (US) |
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Pages (from-to) | 1-41 |

Number of pages | 41 |

Journal | Advances in Theoretical and Mathematical Physics |

Volume | 5 |

Issue number | 6 |

State | Published - Nov 1 2001 |

### ASJC Scopus subject areas

- Mathematics(all)
- Physics and Astronomy(all)

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## Cite this

Baik, J., Deift, P., McLaughlin, K., Miller, P., & Zhou, X. (2001). Optimal tail estimates for directed last passage site percolation with geometric random variables.

*Advances in Theoretical and Mathematical Physics*,*5*(6), 1-41.