Asymptotics of Hankel Determinants for Some Freud Weights

Chao Min, Liwei Wang, Yang Chen

Published 2023-08-07Version 1

In this paper, we study the large $n$ asymptotics of Hankel determinants generated by some nontrivial Freud weight functions. These are obtained from the integral representations of the Hankel determinants in terms of the recurrence coefficients for the corresponding orthogonal polynomials and with the aid of a recent result of Claeys, Krasovsky and Minakov [Commun. Math. Phys. 402 (2023) 833-894]. We also derive the large $n$ asymptotics of the sub-leading coefficients and the squares of $L^2$-norm of the monic orthogonal polynomials.