منابع مشابه
On Asymptotics for the Airy Process
The Airy process t → A(t), introduced by Prähofer and Spohn, is the limiting stationary process for a polynuclear growth model. Adler and van Moerbeke found a PDE in the variables s1, s2 and t for the probability Pr (A(0) ≤ s1, 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 fo...
متن کاملAsymptotics for the Covariance of the Airy 2 Process
In this paper we compute some of the higher order terms in the asymptotic behavior of the two point function P(A2(0)≤ s1,A2(t)≤ s2), extending the previous work of Adler and van Moerbeke (arXiv:math.PR/0302329; Ann. Probab. 33, 1326–1361, 2005) and Widom (J. Stat. Phys. 115, 1129–1134, 2004). We prove that it is possible to represent any order asymptotic approximation as a polynomial and integr...
متن کاملAiry Asymptotics: The logarithmic derivative and its reciprocal
We consider the asymptotic expansion of the logarithmic derivative of the Airy function , and also its reciprocal ) ( Ai / ) ( i A z z ) ( i A / ) ( Ai z z , as z . In particular, we derive simple, closed-form solutions for the coefficients which appear in these expansions, of interest since they are encountered in a wide variety of problems. The solutions are presented as Mellin transf...
متن کاملA PDE for the joint distributions of the Airy Process
In this paper, we answer a question posed by Kurt Johansson, to find a PDE for the joint distribution of the Airy Process. The latter is a continuous stationary process, describing the motion of the outermost particle of the Dyson Brownian motion, when the number of particles get large, with space and time appropriately rescaled. The question reduces to an asymptotic analysis on the equation, g...
متن کاملA System of Differential Equations for the Airy Process
The Airy process τ → Aτ is characterized by its finite-dimensional distribution functions Pr (Aτ1 < ξ1, . . . , Aτm < ξm) . For m = 1 it is known that Pr (Aτ < ξ) is expressible in terms of a solution to Painlevé II. We show that each finite-dimensional distribution function is expressible in terms of a solution to a system of differential equations.
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ژورنال
عنوان ژورنال: Journal of Statistical Physics
سال: 2004
ISSN: 0022-4715
DOI: 10.1023/b:joss.0000022384.58696.61