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

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

2011-09-29

arxiv.org/abs/1109.6463v1

Elect. Comm. in Probab. 16 (2011), 706-711

Mathematics

Probability

7 pages

Scientific paper

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 Schr\"{o}dinger operators. The similar question for Hankel matrices remains open.

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