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Article Dans Une Revue Electronic Communications in Probability Année : 2005

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

Résumé

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 Tusnàdy.
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Dates et versions

hal-00003004 , version 1 (06-10-2004)

Identifiants

  • HAL Id : hal-00003004 , version 1

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Thierry Bodineau, James Martin. A universality property for last-passage percolation paths close to the axis. Electronic Communications in Probability, 2005, 10, pp.105 - 112. ⟨hal-00003004⟩
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