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

Jinho Baik, Percy Deift, Kenneth D T Mclaughlin, Peter Miller, Xin Zhou

Research output: Contribution to journalArticle

38 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)1-41
Number of pages41
JournalAdvances in Theoretical and Mathematical Physics
Volume5
Issue number6
StatePublished - Nov 2001
Externally publishedYes

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random variables
Tail
Random variable
estimates
Estimate
Moderate Deviations
Scaling Laws
scaling laws
Probability Distribution
Model
Fluctuations
Moment
moments
deviation
Imply
Path

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Mathematics(all)

Cite this

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.

In: Advances in Theoretical and Mathematical Physics, Vol. 5, No. 6, 11.2001, p. 1-41.

Research output: Contribution to journalArticle

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