On Concentration of Empirical Measures and Convergence to the Semi-circle Law

S. G. Bobkov; F. Götze; A. N. Tikhomirov

doi:10.1007/s10959-010-0286-7

On Concentration of Empirical Measures and Convergence to the Semi-circle Law

S. G. Bobkov, F. Götze, A. N. Tikhomirov

School of Mathematics

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

17 Scopus citations

Abstract

Concentration properties of the general empirical distribution functions and the rate of convergence of spectral empirical distributions to the semi-circle law in the case of symmetric high-dimensional random matrices are studied under Poincaré-type inequalities.

Original language	English (US)
Pages (from-to)	792-823
Number of pages	32
Journal	Journal of Theoretical Probability
Volume	23
Issue number	3
DOIs	https://doi.org/10.1007/s10959-010-0286-7
State	Published - 2010

Bibliographical note

Funding Information:
Research partially supported by NSF grant DMS-0706866, SFB 701, RFBR grant N07-01-00583-a, and RF grant of the leading scientific schools NSh-638.2008.1.

Keywords

Empirical distributions
Poincaré-type inequalities
Random matrices
Semi-circle law
Spectrum

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10.1007/s10959-010-0286-7

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title = "On Concentration of Empirical Measures and Convergence to the Semi-circle Law",

abstract = "Concentration properties of the general empirical distribution functions and the rate of convergence of spectral empirical distributions to the semi-circle law in the case of symmetric high-dimensional random matrices are studied under Poincar{\'e}-type inequalities.",

keywords = "Empirical distributions, Poincar{\'e}-type inequalities, Random matrices, Semi-circle law, Spectrum",

author = "Bobkov, {S. G.} and F. G{\"o}tze and Tikhomirov, {A. N.}",

note = "Funding Information: Research partially supported by NSF grant DMS-0706866, SFB 701, RFBR grant N07-01-00583-a, and RF grant of the leading scientific schools NSh-638.2008.1.",

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doi = "10.1007/s10959-010-0286-7",

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AU - Bobkov, S. G.

AU - Götze, F.

AU - Tikhomirov, A. N.

N1 - Funding Information: Research partially supported by NSF grant DMS-0706866, SFB 701, RFBR grant N07-01-00583-a, and RF grant of the leading scientific schools NSh-638.2008.1.

PY - 2010

Y1 - 2010

N2 - Concentration properties of the general empirical distribution functions and the rate of convergence of spectral empirical distributions to the semi-circle law in the case of symmetric high-dimensional random matrices are studied under Poincaré-type inequalities.

AB - Concentration properties of the general empirical distribution functions and the rate of convergence of spectral empirical distributions to the semi-circle law in the case of symmetric high-dimensional random matrices are studied under Poincaré-type inequalities.

KW - Empirical distributions

KW - Poincaré-type inequalities

KW - Random matrices

KW - Semi-circle law

KW - Spectrum

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JO - Journal of Theoretical Probability

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ER -

On Concentration of Empirical Measures and Convergence to the Semi-circle Law

Abstract

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Keywords

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