A universality property for last-passage percolation paths close to the axisReport as inadecuate




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1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires 2 LIAFA - Laboratoire d-informatique Algorithmique : Fondements et Applications

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 $n\to\infty$ 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.

Mots-clés : Last-passage percolation Queueing theory





Author: Thierry Bodineau - James Martin -

Source: https://hal.archives-ouvertes.fr/



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