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A Universality Property for Last-Passage Percolation Paths Close to the Axis
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Thierry Bodineau, Université Pierre et Marie Curie, France
James Martin, Université Paris 7, France
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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
$(n,n^a)$. We show that, for suitable $a$ (depending on $p$), this
quantity,
appropriately scaled, converges in distribution as $ntoinfty$ 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.
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Full text: PDF
Pages: 105-112
Published on: June 9, 2005
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