The smallest eigenvalue of large Hankel matrices associated with a singularly perturbed Gaussian weight

Wang, Dan; Zhu, Mengkun; Chen, Yang

doi:10.1090/proc/15757

The smallest eigenvalue of large Hankel matrices associated with a singularly perturbed Gaussian weight
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by Dan Wang, Mengkun Zhu and Yang Chen PDF

Proc. Amer. Math. Soc. 150 (2022), 153-160 Request permission

Abstract:

An asymptotic expression for the polynomials $\mathcal {P}_n(z)$, $z\notin (-\infty ,\infty )$, orthonormal with respect to a singularly perturbed Gaussian weight, $\exp (-z^2-t/z^2),~z\in (-\infty ,\infty ),~t>0$, is established. Based on this, the asymptotic behavior of the smallest eigenvalue of the Hankel matrix generated by the weight is described.

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