Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
LOCAL LAW AND TRACY-WIDOM LIMIT FOR SPARSE SAMPLE COVARIANCE MATRICES
Korea Adv Inst Sci & Technol, Dept Math Sci, Daejeon 34141, South Korea..
Korea Adv Inst Sci & Technol, Dept Math Sci, Daejeon 34141, South Korea..
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2019 (English)In: The Annals of Applied Probability, ISSN 1050-5164, E-ISSN 2168-8737, Vol. 29, no 5, p. 3006-3036Article in journal (Refereed) Published
Abstract [en]

We consider spectral properties of sparse sample covariance matrices, which includes biadjacency matrices of the bipartite Erdos-Renyi graph model. We prove a local law for the eigenvalue density up to the upper spectral edge. Under a suitable condition on the sparsity, we also prove that the limiting distribution of the rescaled, shifted extremal eigenvalues is given by the GOE Tracy-Widom law with an explicit formula on the deterministic shift of the spectral edge. For the biadjacency matrix of an Erdos-Renyi graph with two vertex sets of comparable sizes M and N, this establishes Tracy-Widom fluctuations of the second largest eigenvalue when the connection probability p is much larger than N-2/3 with a deterministic shift of order (Np)(-1).

Place, publisher, year, edition, pages
INST MATHEMATICAL STATISTICS , 2019. Vol. 29, no 5, p. 3006-3036
Keywords [en]
High-dimensional sample covariance matrices, local law, Tracy-Widom distribution
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-263354DOI: 10.1214/19-AAP1472ISI: 000491159000011Scopus ID: 2-s2.0-85075059742OAI: oai:DiVA.org:kth-263354DiVA, id: diva2:1371247
Note

QC 20191119

Available from: 2019-11-19 Created: 2019-11-19 Last updated: 2020-02-04Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full textScopus

Authority records BETA

Schnelli, Kevin

Search in DiVA

By author/editor
Schnelli, Kevin
By organisation
Mathematical Statistics
In the same journal
The Annals of Applied Probability
Probability Theory and Statistics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf