Painlevé III asymptotics of Hankel determinants for a singularly perturbed Laguerre weight
Painlevé III asymptotics of Hankel determinants for a singularly perturbed Laguerre weight
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DOI：
10.1016/j.jat.2014.12.003
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发表时间：
2014-07
期刊：
影响因子：
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通讯作者：
Shuai‐Xia Xu;D. Dai;Yuqiu Zhao
中科院分区：
文献类型：
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作者：
Shuai‐Xia Xu;D. Dai;Yuqiu Zhao
In this paper, we consider the Hankel determinants associated with the singularly perturbed Laguerre weight w (x)= x α e− x− t/x, x∈(0,∞), t> 0 and α> 0. When the matrix size n→∞, we obtain an asymptotic formula for the Hankel determinants, valid uniformly for t∈(0, d], d> 0 fixed. A particular Painlevé III transcendent is involved in the approximation, as well as in the large-n asymptotics of the leading coefficients and recurrence coefficients for the corresponding perturbed Laguerre polynomials. The derivation is based on the asymptotic results in an earlier paper of the authors, obtained by using the Deift–Zhou nonlinear steepest descent method.
