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A universality property for last-passage percolation paths close to the axis | | Thierry Bodineau
; James B. Martin
; | | Date: |
3 Oct 2004 | | Subject: | Probability MSC-class: 60K35 | math.PR | | Abstract: | 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 $ig(n,n^{lfloor a
floor}ig)$. We show that, for suitable $a$ (depending on $p$), this quantity, appropriately scaled, converges in distribution as $n oinfty$ 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 Komlós, Major and Tusnády. | | Source: | arXiv, math.PR/0410042 | | Services: | Forum | Review | PDF | Favorites | |
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