DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Lee, Ji Oon | - |
dc.contributor.advisor | 이지운 | - |
dc.contributor.author | Park, Jaewhi | - |
dc.date.accessioned | 2023-06-22T19:33:50Z | - |
dc.date.available | 2023-06-22T19:33:50Z | - |
dc.date.issued | 2022 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=1007826&flag=dissertation | en_US |
dc.identifier.uri | http://hdl.handle.net/10203/308565 | - |
dc.description | 학위논문(박사) - 한국과학기술원 : 수리과학과, 2022.8,[iv, 108 p. | - |
dc.description | ] | - |
dc.description.abstract | In this paper, we study the limiting distribution of extremal eigenvalues of two different types of random matrices models. The first model is the sample covariance matrix model which is defined by multiplications of sample matrix and population matrix. We show that if the limiting spectral distribution of the population matrix has convex decay at the rightmost edge, then the order statistics of the population matrix determine the limiting distribution of the largest eigenvalue of the model. The second matrix model is the sum of Hermitian matrices with a Haar unitary conjugation. We prove that the law of the largest eigenvalue of the matrix weakly converges to the GUE Tracy-Widom distribution. As a result, we establish the edge universality for the model. | - |
dc.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.subject | Random matrix theory▼aSample covariance matrix▼aedge universality▼afree convolution | - |
dc.subject | 랜덤행렬이론▼a표본 공분산 행렬▼a모서리 보편성▼a자유 합성곱 | - |
dc.title | Extremal eigenvalues of sums and products of random matrices | - |
dc.title.alternative | 랜덤 행렬의 합과 곱의 극대 고유값 | - |
dc.type | Thesis(Ph.D) | - |
dc.identifier.CNRN | 325007 | - |
dc.description.department | 한국과학기술원 :수리과학과, | - |
dc.contributor.alternativeauthor | 박재휘 | - |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.