Absolute continuity of the limiting eigenvalue distribution of the random Toeplitz matrix
Probability
2022-04-27 v1
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 Schr\"{o}dinger operators. The similar question for Hankel matrices remains open.
Keywords
Cite
@article{arxiv.1109.6463,
title = {Absolute continuity of the limiting eigenvalue distribution of the random Toeplitz matrix},
author = {Arnab Sen and Bálint Virág},
journal= {arXiv preprint arXiv:1109.6463},
year = {2022}
}
Comments
7 pages