This paper provides a new proof of a theorem of Chandler-Wilde, Chonchaiya, and Lindner that the spectra of a certain class of infinite, random, tridiagonal matrices contain the unit disc almost surely. It also obtains an analogous result for a more general class of random matrices whose spectra contain a hole around the origin. The presence of the hole forces substantial changes to the analysis.
Cite this article
Simon N. Chandler-Wilde, E. Brian Davies, Spectrum of a Feinberg–Zee random hopping matrix. J. Spectr. Theory 2 (2012), no. 2, pp. 147–179DOI 10.4171/JST/25