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math.SP2016
Spectral asymptotics for Kac-Murdock-Szegő matrices
Alain Bourget, Allen Alvarez Loya, Tyler McMillen
Szegő's First Limit Theorem provides the limiting statistical distribution (LSD) of the eigenvalues of large Toeplitz matrices. Szegő's Second (or Strong) Limit Theorem for Toeplit…
math.SP2016
Asymptotics of determinants of discrete Schrödinger operators
Alain Bourget, Tyler McMillen
We consider the asymptotics of the determinants of large discrete Schrödinger operators, i.e. "discrete Laplacian diagonal": \[T_n(f) = -[δ_{j,j+1}+δ_{j+1,j}] + \mbox{diag}\lef…
math.SP2008
A note on the eigenvalues of double band matrices
Tyler McMillen
We consider matrices containing two diagonal bands of positive entries. We show that all eigenvalues of such matrices are of the form , where is a nonnegative real number…