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

Arnab Sen; Bálint Virág

doi:10.1214/ECP.v16-1675

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

Arnab Sen
, Bálint Virág

School of Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

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�dinger operators. The similar question for Hankel matrices remains open.

Original language	English (US)
Pages (from-to)	706-711
Number of pages	6
Journal	Electronic Communications in Probability
Volume	16
DOIs	https://doi.org/10.1214/ECP.v16-1675
State	Published - Jan 1 2011

Keywords

Eigenvalue distribution
Spectral averaging
Toeplitz matrix

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10.1214/ECP.v16-1675

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title = "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 Schr�dinger operators. The similar question for Hankel matrices remains open.",

keywords = "Eigenvalue distribution, Spectral averaging, Toeplitz matrix",

author = "Arnab Sen and B{\'a}lint Vir{\'a}g",

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doi = "10.1214/ECP.v16-1675",

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T1 - Absolute continuity of the limiting eigenvalue distribution of the random toeplitz matrix

AU - Sen, Arnab

AU - Virág, Bálint

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Y1 - 2011/1/1

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AB - 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�dinger operators. The similar question for Hankel matrices remains open.

KW - Eigenvalue distribution

KW - Spectral averaging

KW - Toeplitz matrix

UR - https://www.scopus.com/pages/publications/83255192899

UR - https://www.scopus.com/pages/publications/83255192899#tab=citedBy

U2 - 10.1214/ECP.v16-1675

DO - 10.1214/ECP.v16-1675

M3 - Article

AN - SCOPUS:83255192899

SN - 1083-589X

VL - 16

SP - 706

EP - 711

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

ER -

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

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