Local law and Tracy-Widom limit for sparse random matrices

Cited 7 time in webofscience Cited 0 time in scopus
  • Hit : 152
  • Download : 0
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)..
Publisher
SPRINGER HEIDELBERG
Issue Date
2018-06
Language
English
Article Type
Article
Citation

PROBABILITY THEORY AND RELATED FIELDS, v.171, no.1-2, pp.543 - 616

ISSN
0178-8051
DOI
10.1007/s00440-017-0787-8
URI
http://hdl.handle.net/10203/242403
Appears in Collection
MA-Journal Papers(저널논문)
Files in This Item
There are no files associated with this item.
This item is cited by other documents in WoS
⊙ Detail Information in WoSⓡ Click to see webofscience_button
⊙ Cited 7 items in WoS Click to see citing articles in records_button

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0