Asymptotics of Tracy-Widom distributions and the total integral of a Painlevé II function
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Publication:934625
DOI10.1007/S00220-008-0433-5zbMATH Open1221.33032arXiv0704.3636OpenAlexW3099473530MaRDI QIDQ934625
Author name not available (Why is that?)
Publication date: 30 July 2008
Published in: (Search for Journal in Brave)
Abstract: The Tracy-Widom distribution functions involve integrals of a Painlev'e II function starting from positive infinity. In this paper, we express the Tracy-Widom distribution functions in terms of integrals starting from minus infinity. There are two consequences of these new representations. The first is the evaluation of the total integral of the Hastings-McLeod solution of the Painlev'e II equation. The second is the evaluation of the constant term of the asymptotic expansions of the Tracy-Widom distribution functions as the distribution parameter approaches minus infinity. For the GUE Tracy-Widom distribution function, this gives an alternative proof of the recent work of Deift, Its, and Krasovsky. The constant terms for the GOE and GSE Tracy-Widom distribution functions are new.
Full work available at URL: https://arxiv.org/abs/0704.3636
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