On universality of bulk local regime of the Hermitian sample covariance matrices

Tatyana Shcherbina

doi:10.1063/1.3498377

On universality of bulk local regime of the Hermitian sample covariance matrices

Tatyana Shcherbina

Mathematics

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

Abstract

We consider the Hermitian sample covariance matrices H_n=m^-1Σ_n^1/2A_m,nA_m,n^*Σ_n^1/2 in which Σ_n is a positive definite Hermitian matrix (possibly random) and A_m,n is a n×m complex Gaussian random matrix (independent of Σ_n), and m→∞, n→∞, such that mn^-1→c>1. Assuming that the normalized counting measure of Σ_n converges weakly (in probability) to a nonrandom measure N⁽⁰⁾ with a bounded support, we prove the universality of the local eigenvalue statistics in the bulk of the limiting spectrum of H_n.

Original language	English (US)
Article number	103516
Journal	Journal of Mathematical Physics
Volume	51
Issue number	10
DOIs	https://doi.org/10.1063/1.3498377
State	Published - Oct 2010

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Access to Document

10.1063/1.3498377

Cite this

@article{2ff70f41a6314350973c8a11650428da,

title = "On universality of bulk local regime of the Hermitian sample covariance matrices",

abstract = "We consider the Hermitian sample covariance matrices Hn=m-1Σn1/2Am,nAm,n*Σn1/2 in which Σn is a positive definite Hermitian matrix (possibly random) and Am,n is a n×m complex Gaussian random matrix (independent of Σn), and m→∞, n→∞, such that mn-1→c>1. Assuming that the normalized counting measure of Σn converges weakly (in probability) to a nonrandom measure N(0) with a bounded support, we prove the universality of the local eigenvalue statistics in the bulk of the limiting spectrum of Hn.",

author = "Tatyana Shcherbina",

year = "2010",

month = oct,

doi = "10.1063/1.3498377",

language = "English (US)",

volume = "51",

journal = "Journal of Mathematical Physics",

issn = "0022-2488",

publisher = "American Institute of Physics",

number = "10",

}

TY - JOUR

T1 - On universality of bulk local regime of the Hermitian sample covariance matrices

AU - Shcherbina, Tatyana

PY - 2010/10

Y1 - 2010/10

N2 - We consider the Hermitian sample covariance matrices Hn=m-1Σn1/2Am,nAm,n*Σn1/2 in which Σn is a positive definite Hermitian matrix (possibly random) and Am,n is a n×m complex Gaussian random matrix (independent of Σn), and m→∞, n→∞, such that mn-1→c>1. Assuming that the normalized counting measure of Σn converges weakly (in probability) to a nonrandom measure N(0) with a bounded support, we prove the universality of the local eigenvalue statistics in the bulk of the limiting spectrum of Hn.

AB - We consider the Hermitian sample covariance matrices Hn=m-1Σn1/2Am,nAm,n*Σn1/2 in which Σn is a positive definite Hermitian matrix (possibly random) and Am,n is a n×m complex Gaussian random matrix (independent of Σn), and m→∞, n→∞, such that mn-1→c>1. Assuming that the normalized counting measure of Σn converges weakly (in probability) to a nonrandom measure N(0) with a bounded support, we prove the universality of the local eigenvalue statistics in the bulk of the limiting spectrum of Hn.

UR - http://www.scopus.com/inward/record.url?scp=78149416961&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78149416961&partnerID=8YFLogxK

U2 - 10.1063/1.3498377

DO - 10.1063/1.3498377

M3 - Article

AN - SCOPUS:78149416961

SN - 0022-2488

VL - 51

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 10

M1 - 103516

ER -

On universality of bulk local regime of the Hermitian sample covariance matrices

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this