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Local law and Tracy-Widom limit for sparse random matrices
Korea Adv Inst Sci & Technol, Daejeon, South Korea..
KTH. IST Austria, Klosterneuburg, Austria..
2018 (English)In: Probability theory and related fields, ISSN 0178-8051, E-ISSN 1432-2064, Vol. 171, no 1-2, p. 543-616Article in journal (Refereed) Published
Abstract [en]

We consider spectral properties and the edge universality of sparse random matrices, the class of random matrices that includes the adjacency matrices of the ErdAs-R,nyi graph model G(N, p). We prove a local law for the eigenvalue density up to the spectral edges. Under a suitable condition on the sparsity, we also prove that the rescaled extremal eigenvalues exhibit GOE Tracy-Widom fluctuations if a deterministic shift of the spectral edge due to the sparsity is included. For the adjacency matrix of the ErdAs-R,nyi graph this establishes the Tracy-Widom fluctuations of the second largest eigenvalue when p is much larger than wth a deterministic shift of order (Np)(-1)..

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2018. Vol. 171, no 1-2, p. 543-616
Keywords [en]
Local law, Sparse random matrices, Erdos-Renyi graph
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-229009DOI: 10.1007/s00440-017-0787-8ISI: 000432129600012OAI: oai:DiVA.org:kth-229009DiVA, id: diva2:1211746
Funder
EU, European Research Council, 338804
Note

QC 20180531

Available from: 2018-05-31 Created: 2018-05-31 Last updated: 2018-05-31Bibliographically approved

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Schnelli, Kevin

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