DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Jung, Paul | - |
dc.contributor.advisor | 폴정 | - |
dc.contributor.author | Lee, Jaehun | - |
dc.date.accessioned | 2023-06-22T19:33:53Z | - |
dc.date.available | 2023-06-22T19:33:53Z | - |
dc.date.issued | 2022 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=1007829&flag=dissertation | en_US |
dc.identifier.uri | http://hdl.handle.net/10203/308573 | - |
dc.description | 학위논문(박사) - 한국과학기술원 : 수리과학과, 2022.8,[iv, 136 p. :] | - |
dc.description.abstract | We consider the normalized adjacency matrix $H$ of Erd\H{o}s-R\'{e}nyi graphs $\mathcal{G}(N,p)$ and assume $N^{\epsilon} < pN < N^{1-\epsilon}$. When $pN < N^{1/3-\epsilon}$, it was recently shown that leading order fluctuations of extreme eigenvalues of $H$ are given by a single random variable associated with the total degree of the graph (Huang-Landon-Yau, 2020 | - |
dc.description.abstract | He-Knowles, 2021). We construct a sequence of random correction terms to capture higher (sub-leading) order fluctuations of extreme eigenvalues of $H$. Using these random correction terms, we prove a local law up to a (randomly) shifted edge and recover the rigidity of extreme eigenvalues under some random corrections in the sparse regime $pN > N^{\epsilon}$. In another direction, we investigate the noise sensitivity of the top eigenvector of $H$. Let $v$ be the top eigenvector of $H$. We resample $k$ uniformly randomly chosen entries of the matrix and obtain another realization of the random matrix with top eigenvector $v^{[k]}$. Building on recent results on sparse random matrices and a noise sensitivity analysis previously developed for Wigner matrices, we prove that, if $pN\geq N^{2/9}$, with high probability, when $k \ll N^{5/3}$, the vectors $v$ and $v^{[k]}$ are almost collinear and, on the contrary, when $k\gg N^{5/3}$, the vectors $v$ and $v^{[k]}$ are almost orthogonal. | - |
dc.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.subject | sparse random graphs▼aErdos-Renyi graph▼arandom matrix theory▼anoise sensitivity | - |
dc.subject | 희소 랜덤 그래프▼a에르되시-레니 그래프▼a랜덤 행렬 이론▼a노이즈 민감도 | - |
dc.title | Spectrum of sparse random graphs and related problems | - |
dc.title.alternative | 희소 랜덤 그래프의 스펙트럼과 관련 문제들 | - |
dc.type | Thesis(Ph.D) | - |
dc.identifier.CNRN | 325007 | - |
dc.description.department | 한국과학기술원 :수리과학과, | - |
dc.contributor.alternativeauthor | 이재훈 | - |
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