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Название: On Asymptotics for the Airy Process
Автор: Widom H.
Journal of Statistical Physics, Vol. 115, Nos. 3/4, May 2004, p. 1129-1134.
The Airy process t -> A(t), introduced by Prahofer 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 Pr(A(0) \< s_1, A(t) \< s2). Using this they were able, assuming the truth of a certain conjecture and appropriate uniformity, to obtain the first few terms of an asymptotic expansion for this probability as t -> oo, 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 С A. Tracy in the derivation of the Painleve II representation for the distribution function F_2 plus a few others obtained in the same way.