Overcrowding asymptotics for the $\operatorname{Sine}_{\beta}$ process
نویسندگان
چکیده
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...
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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...
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ژورنال
عنوان ژورنال: Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
سال: 2017
ISSN: 0246-0203
DOI: 10.1214/16-aihp752