Event Details

Speaker: Yang Chen Title: The smallest eigenvalue of the Hankel matrices associated with a perturbed Jacobi weight

Abstract: We study the large N behavior of the smallest eigenvalue λ_N of the (N+1) × (N+1) Hankel matrix generated by the γ dependent Jacobi weight w(z,γ)=exp(-γz)z^α (1-z)^β, where z∊[0,1], γ∊ℝ, and α,β>-1. Applying the arguments of Szegö, Widom and Wilf, we obtain the asymptotic representation of the orthonormal polynomials P_N(z) for z∊ ℂ \ [0,1], with the same weight. Using the polynomials, we obtain the theoretical expression of λ_N, for large N. Joint work with Yuxi Wang (University of Macau).