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


 
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1. Title Title of document A Universality Property for Last-Passage Percolation Paths Close to the Axis
 
2. Creator Author's name, affiliation, country Thierry Bodineau; Université Pierre et Marie Curie, France
 
2. Creator Author's name, affiliation, country James Martin; Université Paris 7, France
 
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4. Description 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 Tusnády.
 
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7. Date (YYYY-MM-DD) 2005-06-09
 
8. Type Status & genre Peer-reviewed Article
 
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9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1139
 
10. Identifier Digital Object Identifier 10.1214/ECP.v10-1139
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 10
 
12. Language English=en
 
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