Mathematical Physics and Harmonic Analysis Seminar

Date: September 20, 2019

Time: 1:50PM - 2:50PM

Location: BLOC 628

Speaker: Junho Yang, Texas A&M University, Statistics

Title: Rate of convergence in Szego limit theorems

Abstract: We discuss an improved rate of convergence of eigenvalues of Hermitian Toeplitz matrices originated from Szego's limiting eigenvalue distribution theorem. The proof consists of two steps: 1) provide point-wise asymptotics of all eigenvalues of banded Hermitian matrices; 2) Approximate general n-by-n Toeplitz matrix with p-diagonal banded Hermitian matrix in the sense of the "best predictive" function, and provide an entrywise 1-norm error bound. Our results can be used to calculate the exact bound of the Whittle's likelihood approximation, and approximations for the inverse of Toeplitz matrices.

Joint work with Suhasini Subbarao (TAMU Statistics).