Outliers in spectrum of sparse Wigner matrices

In this paper, we study the effect of sparsity on the appearance of outliers in the semi‐circular law. Let (Wn)n=1∞ be a sequence of random symmetric matrices such that each Wn is n × n with i.i.d. entries above and on the main diagonal equidistributed with the product bnξ, where ξ is a real centere...

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Bibliographic Details

Published in:	Random structures & algorithms Vol. 58; no. 3; pp. 517 - 605
Main Authors:	Tikhomirov, Konstantin, Youssef, Pierre
Format:	Journal Article
Language:	English
Published:	New York John Wiley & Sons, Inc 01.05.2021 Wiley Subscription Services, Inc Wiley
Subjects:	BBP phase transition Convergence Eigenvalues Erdos‐Renyi graph Mathematical analysis Mathematics Matrix methods moment method outliers Phase transitions Probability Random variables Sparse matrices Sparsity spectral gap
ISSN:	1042-9832, 1098-2418
Online Access:	Get full text
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