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

By T. Bodineau, James B. Martin. 2004

72 citations recorded by the source corpus.

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 Komlos, Major and Tusnady.

Subfields: Artificial Intelligence, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/bddd8de2cec909ade6c3274f14632547e45b2b3c

Citations in the corpus

• A generalization of the Lindeberg principle (2005, unknown): “It was recently observed by Toufic Suidan [18] that the results in [5] can be used to give an immediate proof of the universality of last passage percolation in thin rectangles (originally a result of [3] and [4]).”
• Universality for mathematical and physical systems (2006, unknown): “.i.d.’s, suitably centered and scaled, performs operation X on them, and then takes the limit in distribution, the outcome should be F 1, or F 2, etc. Interesting progress has been made recently (see [BodMar] and [BaiSui]) on identifying X for F 2. For a different approachto the results in [BodMar] a”