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Perturbed Hankel Determinants

Estelle Basor·Yang Chen
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Abstract

In this short note, we compute, for large n the determinant of a class of n x n Hankel matrices, which arise from a smooth perturbation of the Jacobi weight. For this purpose, we employ the same idea used in previous papers, where the unknown determinant, D_n[w_{\alpha,\beta}h] is compared with the known determinant D_n[w_{\alpha,\beta}]. Here w_{\alpha,\beta} is the Jacobi weight and w_{\alpha,\beta}h, where h=h(x),x\in[-1,1] is strictly positive and real analytic, is the smooth perturbation on the Jacobi weight w_{\alpha,\beta}(x):=(1-x)^\alpha (1+x)^\beta. Applying a previously known formula on the distribution function of linear statistics, we compute the large n asymptotics of D_n[w_{\alpha,\beta}h] and supply a missing constant of the expansion.

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Estelle Basor, Yang Chen. 2005-09-19. Perturbed Hankel Determinants. https://doi.org/10.1088/0305-4470/38/47/004

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