2 citations · 3 across the 5 of their papers we have counts for
6 papers
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…
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…
Ballistic Orbits and Front Speed Enhancement for ABC Flows
Tyler McMillen, Jack Xin, Yifeng Yu +1
We study the two main types of trajectories of the ABC flow in the near-integrable regime: spiral orbits and edge orbits. The former are helical orbits which are perturbations of s…
Interlacing and asymptotic properties of Stieltjes polynomials
A. Bourget, T. McMillen
Polynomial solutions to the generalized Lamé equation, the \textit{Stieltjes polynomials}, and the associated \textit{Van Vleck polynomials} have been studied since the 1830's, beg…
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…
Interlacing and non-orthogonality of spectral polynomials for the Lamé operator
A. Bourget, T. McMillen, A. Vargas
Polynomial solutions to the generalized Lamé equation, the Stieltjes polynomials, and the associated Van Vleck polynomials have been studied since the 1830's in various contexts in…