Sparse random graphs: Eigenvalues and eigenvectors |
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| Authors: | Linh V. Tran Van H. Vu Ke Wang |
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| Affiliation: | Department of Mathematics, Rutgers, Piscataway, New Jersey 08854 |
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| Abstract: | In this paper, we prove the semi‐circular law for the eigenvalues of regular random graph Gn,d in the case d →∞, complementing a previous result of McKay for fixed d. We also obtain a upper bound on the infinity norm of eigenvectors of Erd?s–Rényi random graph G(n,p), answering a question raised by Dekel–Lee–Linial. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2012 |
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| Keywords: | infinity norm of eigenvector regular random graphs semi‐circular law sparse random matrix |
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