On Asymptotics for the Airy Process

Details On Asymptotics for the Airy Process On Asymptotics for the Airy Process

2003-08-16

arxiv.org/abs/math/0308157v1

Mathematics

Probability

5 pages, LaTex file

Scientific paper

10.1023/B:JOSS.0000022384.58696.

The Airy process A(t), introduced by Pr\"ahofer and Spohn, is the limiting stationary process for a polynuclear growth model. Adler and van Moerbeke found a PDE in the variables s_1, s_2, and t for the probability that A(0)infinity, with fixed s_1 and s_2. We shall show that the expansion can be obtained by using the Fredholm determinant representation for the probability. The main ingredients are formulas obtained by the author and C. A. Tracy in the derivation of the Painlev\'e II representation for the distribution function F_2 plus a few others obtained in the same way.

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