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

Publication
, Journal Article

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

Published in: Advances in Theoretical and Mathematical Physics

January 1, 2001

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.

### Duke Scholars

## Published In

Advances in Theoretical and Mathematical Physics

## DOI

## EISSN

1095-0753

## ISSN

1095-0761

## Publication Date

January 1, 2001

## Volume

5

## Issue

6

## Start / End Page

1207 / 1250

## Related Subject Headings

- Nuclear & Particles Physics
- 0206 Quantum Physics
- 0105 Mathematical Physics

### Citation

APA

Chicago

ICMJE

MLA

NLM

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), 1207–1250. https://doi.org/10.4310/atmp.2001.v5.n6.a7Baik, J., P. Deift, K. McLaughlin, P. Miller, and X. Zhou. “Optimal tail estimates for directed last passage site percolation with geometric random variables.”

*Advances in Theoretical and Mathematical Physics*5, no. 6 (January 1, 2001): 1207–50. https://doi.org/10.4310/atmp.2001.v5.n6.a7.Baik J, Deift P, McLaughlin K, Miller P, Zhou X. Optimal tail estimates for directed last passage site percolation with geometric random variables. Advances in Theoretical and Mathematical Physics. 2001 Jan 1;5(6):1207–50.

Baik, J., et al. “Optimal tail estimates for directed last passage site percolation with geometric random variables.”

*Advances in Theoretical and Mathematical Physics*, vol. 5, no. 6, Jan. 2001, pp. 1207–50.*Scopus*, doi:10.4310/atmp.2001.v5.n6.a7.Baik J, Deift P, McLaughlin K, Miller P, Zhou X. Optimal tail estimates for directed last passage site percolation with geometric random variables. Advances in Theoretical and Mathematical Physics. 2001 Jan 1;5(6):1207–1250.

## Published In

Advances in Theoretical and Mathematical Physics

## DOI

## EISSN

1095-0753

## ISSN

1095-0761

## Publication Date

January 1, 2001

## Volume

5

## Issue

6

## Start / End Page

1207 / 1250

## Related Subject Headings

- Nuclear & Particles Physics
- 0206 Quantum Physics
- 0105 Mathematical Physics