Sparse random graphs: Eigenvalues and eigenvectors

  title={Sparse random graphs: Eigenvalues and eigenvectors},
  author={Linh V. Tran and Van H. Vu and Ke Wang},
  journal={Random Struct. Algorithms},
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 Erdős-Rényi random graph G(n, p), answering a question raised by Dekel-Lee-Linial. 
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