Sparse random graphs: Eigenvalues and eigenvectors

Authors:
Linh V. Tran;Van H. Vu;Ke Wang
Affiliations:
Department of Mathematics, Rutgers, Piscataway, New Jersey 08854;Department of Mathematics, Rutgers, Piscataway, New Jersey 08854;Department of Mathematics, Rutgers, Piscataway, New Jersey 08854
Venue:
Random Structures & Algorithms
Year:
2013

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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 Erdős–Rényi random graph G(n,p), answering a question raised by Dekel–Lee–Linial. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2012 © 2013 Wiley Periodicals, Inc.