Chandler-Wilde, Simon N.Simon N.Chandler-WildeChonchaiya, RatchanikornRatchanikornChonchaiyaLindner, MarkoMarkoLindner2021-10-252021-10-252010-03-20Operators and Matrices Volume 5, Number 4 (2011), 633-648 5 (4): 633-648 (2010-03-20T18:21:34Z)http://hdl.handle.net/11420/10584The purpose of this paper is to prove that the spectrum of the non-self-adjoint one-particle Hamiltonian proposed by J. Feinberg and A. Zee (Phys. Rev. E 59 (1999), 6433--6443) has interior points. We do this by first recalling that the spectrum of this random operator is the union of the set of ℓ∞ eigenvalues of all infinite matrices with the same structure. We then construct an infinite matrix of this structure for which every point of the open unit disk is an ℓ∞ eigenvalue, this following from the fact that the components of the eigenvector are polynomials in the spectral parameter whose non-zero coefficients are ± 1's, forming the pattern of an infinite discrete Sierpinski triangle.en1846-388620104633648Disordered systemsJacobi matrixRandom matrixSpectral theoryMathematical PhysicsMathematical PhysicsMathematics - Mathematical PhysicsMathematics - Spectral Theory47B80Journal Article10.7153/oam-05-461003.3946v3Other