The smallest eigenvalue of large Hankel matrices generated by a deformed Laguerre weight

We study the asymptotic behavior of the smallest eigenvalue, λ_N, of the Hankel (or moments) matrix denoted by , with respect to the weight . An asymptotic expression of the polynomials orthogonal with w(x) is established. Using this, we obtain the specific asymptotic formulas of λ_N in this paper. Applying a parallel numerical algorithm, we get a variety of numerical results of λ_N corresponding to our theoretical calculations.