### 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) |
---|---|

Pages (from-to) | 1-41 |

Number of pages | 41 |

Journal | Advances in Theoretical and Mathematical Physics |

Volume | 5 |

Issue number | 6 |

State | Published - Nov 2001 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*Advances in Theoretical and Mathematical Physics*,

*5*(6), 1-41.

**Optimal tail estimates for directed last passage site percolation with geometric random variables.** / Baik, Jinho; Deift, Percy; Mclaughlin, Kenneth D T; Miller, Peter; Zhou, Xin.

Research output: Contribution to journal › Article

*Advances in Theoretical and Mathematical Physics*, vol. 5, no. 6, pp. 1-41.

}

TY - JOUR

T1 - Optimal tail estimates for directed last passage site percolation with geometric random variables

AU - Baik, Jinho

AU - Deift, Percy

AU - Mclaughlin, Kenneth D T

AU - Miller, Peter

AU - Zhou, Xin

PY - 2001/11

Y1 - 2001/11

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0242535780&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0242535780&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0242535780

VL - 5

SP - 1

EP - 41

JO - Advances in Theoretical and Mathematical Physics

JF - Advances in Theoretical and Mathematical Physics

SN - 1095-0761

IS - 6

ER -