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

Thierry Bodineau·James B. Martin
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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 $\big(n,n^{\lfloor a \rfloor}\big)$. 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 Komlós, Major and Tusnády.

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Thierry Bodineau, James B. Martin. 2004-10-03. A universality property for last-passage percolation paths close to the axis. https://arxiv.org/abs/math/0410042

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