Electronic Communications in Probability

A Universality Property for Last-Passage Percolation Paths Close to the Axis

Thierry Bodineau and James Martin

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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 $n\to\infty$ 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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Electron. Commun. Probab., Volume 10 (2005), paper no. 11, 105-112.

Accepted: 9 June 2005
First available in Project Euclid: 4 June 2016

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Bodineau, Thierry; Martin, James. A Universality Property for Last-Passage Percolation Paths Close to the Axis. Electron. Commun. Probab. 10 (2005), paper no. 11, 105--112. doi:10.1214/ECP.v10-1139. https://projecteuclid.org/euclid.ecp/1465058076

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