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Hankel determinants for a perturbed Laguerre weight and Painleve V equation
Min Chen1; Yang Chen2; En-Gui Fan1
2018-07-26
Source PublicationarXiv
ISSN2331-8422
Abstract

In this paper, we study Hankel determinants generated from the following perturbed Laguerre weight function, w(x, t) = (x + t) λx α e −x , t > 0, α > 0, α + λ + 1 > 0, x ∈ [0, ∞). Under the double scaling scheme, the random matrix size n → ∞, t → 0, such that s = 4nt is finite, we give the uniform asymptotic approximations of Hankel determinants in terms of a solution of a third-order nonlinear differential equation, which is equivalent to a particular Painlev´e V equation ( PV ). In fact, this PV equation is equivalent to the general Painlev´e III equation. The asymptotic approximations of the leading coefficients and the recurrence coefficients for the corresponding orthogonal polynomials also involve the PV equation. The asymptotic analysis is based on our earlier results by using the Deift-Zhou nonlinear steepest descent method.

Language英語English
Document TypeJournal article
CollectionFaculty of Science and Technology
DEPARTMENT OF MATHEMATICS
Corresponding AuthorEn-Gui Fan
Affiliation1.School of Mathematical Science, Fudan University, Shanghai 200433, P.R. China
2.Faculty of Science and Technology, Department of Mathematics, University of Macau
Recommended Citation
GB/T 7714
Min Chen,Yang Chen,En-Gui Fan. Hankel determinants for a perturbed Laguerre weight and Painleve V equation[J]. arXiv, 2018.
APA Min Chen., Yang Chen., & En-Gui Fan (2018). Hankel determinants for a perturbed Laguerre weight and Painleve V equation. arXiv.
MLA Min Chen,et al."Hankel determinants for a perturbed Laguerre weight and Painleve V equation".arXiv (2018).
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