Absolute continuity of the limiting eigenvalue distribution of the random Toeplitz matrix

Abstract

We show that the limiting eigenvalue distribution of random symmetric Toeplitz matrices is absolutely continuous with density bounded by 8, partially answering a question of Bryc, Dembo and Jiang (2006). The main tool used in the proof is a spectral averaging technique from the theory of random Schrödinger operators. The similar question for Hankel matrices remains open.

7 pages

References in corpus (1)

• The top eigenvalue of the random Toeplitz matrix and the sine kernel