Asymptotic distribution of the spectra of a class of generalized Kac–Murdock–Szegö matrices Original Research Article

We consider symmetric Toeplitz matrices Tn=(tr−s)r,s=1n with tr=αρr+β/ρr, where α and β are real and 0<ρ<1. We give formulas for det(Tn) and Tn−1, and show that if α−β=1 and β≠0 then Tn has eigenvalues λ1n<λ2n