A universality property for last-passage percolation paths close to the axis

We consider a last-passage directed percolation model in $Z_+^2$, with i.i.d. weights whose common distribution has a finite $(2+p)$th moment. We study the fluctuations of the passage time from the origin to the point $\big(n,n^{\lfloor a \rfloor}\big)$. We show that, for suitable $a$ (depending on...

Full description

Saved in:
Bibliographic Details
Main Authors Bodineau, Thierry, Martin, James B
Format Journal Article
LanguageEnglish
Published 03.10.2004
Subjects
Mathematics - Probability
Online AccessGet full text

Cover

More Information
Summary:We consider a last-passage directed percolation model in $Z_+^2$, with i.i.d. weights whose common distribution has a finite $(2+p)$th moment. We study the fluctuations of the passage time from the origin to the point $\big(n,n^{\lfloor a \rfloor}\big)$. We show that, for suitable $a$ (depending on $p$), this quantity, appropriately scaled, converges in distribution as $n\to\infty$ to the Tracy-Widom distribution, irrespective of the underlying weight distribution. The argument uses a coupling to a Brownian directed percolation problem and the strong approximation of Koml\'os, Major and Tusn\'ady.
DOI:10.48550/arxiv.math/0410042