Local law and tracy-widom limit of sparse random matrix models = 희소 랜덤 행렬 모형의 국소적 법칙과 tracy-widom 극한

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We consider spectral properties of sparse random matrix models, which includes sparse sample covariance matrices and sparse stochastic block models. We prove a local law for the eigenvalue density up to the 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.
Advisors
Lee, Ji Oonresearcher이지운researcher
Description
한국과학기술원 :수리과학과,
Publisher
한국과학기술원
Issue Date
2019
Identifier
325007
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수리과학과, 2019.8,[v, 54 p. :]

Keywords

Random matrices▼ahigh dimensional sample covariance matrices▼astochastic block models▼alocal law▼atracy-Widom distribution; 랜덤 행렬▼a고차원 표본 공분산 행렬▼a스토캐스틱 블록 모형▼a국소적 법칙▼aTracy-Widom 분포

URI
http://hdl.handle.net/10203/283241
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=871408&flag=dissertation
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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