Residential College | false |
Status | 已發表Published |
Hankel determinants for a perturbed Laguerre weight and Painleve V equation | |
Min Chen1; Yang Chen2; En-Gui Fan1 | |
2018-07-26 | |
Source Publication | arXiv |
ISSN | 2331-8422 |
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 Type | Journal article |
Collection | Faculty of Science and Technology DEPARTMENT OF MATHEMATICS |
Corresponding Author | En-Gui Fan |
Affiliation | 1.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). |
Files in This Item: | There are no files associated with this item. |
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.
Edit Comment