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…
Spectral Density of Jacobi Matrices with small deviations
Alain Bourget
We present several new asymptotic trace formulas for Jacobi matrices whose coefficients satisfy a small deviation condition. Our results extend most of the existing trace formulas…
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…
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…
Semiclassical Density of States for the Quantum Asymmetric Top
Alfonso F. Agnew, Alain Bourget
In the quantization of a rotating rigid body, a {\it top,} one is concerned with the Hamiltonian operator where An…