Yang Chen

Smallest Eigenvalue of Large Hankel Matrices at Critical Point: How small is small?

Hankel matrices are matrices of moments, (See Heine, Hanbuch der Kugelfunctionen, 1878), plays a fundamental role in approximation theory. Further interest comes from Integrable system, where the parameter appeared in weights (that generates the moments), may be thought of as time variables, which sometimes generates Painleve equation. This talk will focus the smallest eigenvalues associated with the Hankel form, generated by the weight w(x) = exp (- x^{\beta}), x\geq 0, \beta>0.

(Chen, Sikorowski and Zhu, Applied Mathematics and Computation, vol 363 (2019) 124628)