Spectra of sums and products of random matrices랜덤행렬의 합과 곱의 스펙트럼

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We consider two different random matrix models, deformed Wigner matrices and products of unitarily invariant positive definite matrices. For deformed Wigner matrices, that are defined by the sum of Wigner and diagonal matrices, we prove that their linear eigenvalue statistics have asymptotically Gaussian fluctuation as the size of matrices diverges. For the second model, that is the product of two unitarily invariant matrices, we prove an optimal local law around the spectral edge. As its application, we prove eigenvalue rigidity and eigenvector delocalization around the edge.
Advisors
Lee, Ji Oonresearcher이지운researcher
Description
한국과학기술원 :수리과학과,
Country
한국과학기술원
Issue Date
2021
Identifier
325007
Language
eng
Article Type
Thesis(Ph.D)
URI
http://hdl.handle.net/10203/294692
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=962383&flag=dissertation
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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