Wigner Random Matrices with Non-Symmetrically Distributed Entries
Purchase on Springer.com
$39.95 / €34.95 / £29.95*
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.
We show that the spectral radius of an N× N random symmetric matrix with i.i.d. bounded centered but non-symmetrically distributed entries is bounded from above by 2 σ + o(N−6/11+ε), where σ2 is the variance of the matrix entries and ε is an arbitrary small positive number. Our bound improves the earlier results by Z. Füredi and J. Komlós (1981), and Van Vu (2005).
- N. Alon, M. Krivelevich and V. Vu, On the concentration of eigenvalues of random symmetric matrices. Israel J. Math. 131:259–267 (2002).
- L. Arnold, On Wigner’s semicircle law for eigenvalues of random matrices. J. Math. Anal. Appl. 20:262–268 (1967). CrossRef
- Z. D. Bai, Methodologies in spectral analysis of large-dimensional random matrices, a review. Statist. Sinica 9(3):611–677 (1999).
- Z. Füredi and J. Komlós, The eigenvalues of random symmetric matrices. Combinatorica 1(3):233–241 (1981). CrossRef
- A. Guionnet and O. Zeitouni, Concentration of the spectral measure for large matrices. Electron. Comm. Probab. 5:119–136 (2000).
- M. Krivelevich and V. Vu, Approximating the independence number and the chromatic number in expected polynomial time. J. Comb. Optim. 6(2):143–155 (2002). CrossRef
- S. Péché and D. Féral, The largest eigenvalue of some rank one deformation of large Wigner matrices. ArXiv math.PR/0605624, to appear in Commun. Math. Phys. (2006).
- S. Péché, Universality at the soft edge for some white sample covariance matrices ensembles. preprint (2006).
- S. Péché and A. Soshnikov, On the lower bound of the spectral norm of random matrices with independent entries. in preparation (2007).
- Y. Sinai and A. Soshnikov, Central limit theorem for traces of large random symmetric matrices with independent matrix elements. Bol. Soc. Brasil. Mat. (N.S.) 29(1):1–24 (1998). CrossRef
- Y. Sinai and A. Soshnikov, A refinement of Wigner’s semicircle law in a neighborhood of the spectrum edge for random symmetric matrices. Funct. Anal. Appl. 32:114–131 (1998). CrossRef
- A. Soshnikov, Universality at the edge of the spectrum in Wigner random matrices. Commun. Math. Phys. 207:697–733 (1999). CrossRef
- A. Soshnikov, A note on universality of the distribution of the largest eigenvalues in certain sample covariance matrices. J. Stat. Phys. 108:1033–1056 (2002). CrossRef
- C. Tracy and H. Widom, On orthogonal and symplectic matrix ensembles. Commun. Math. Phys. 177:727–754 (1996). CrossRef
- V. H. Vu, Spectral norm of random matrices. In STOC’05: Proceedings of the 37th Annual ACM Symposium on Theory of Computing (2005), pp. 423–430.
- E. Wigner, Characteristic vectors of bordered matrices with infinite dimenisons. Ann. Math. 62:548–564 (1955). CrossRef
- E. Wigner, On the distribution of the roots of certain symmetric matrices. Ann. Math. 68:325–328 (1958). CrossRef
- Wigner Random Matrices with Non-Symmetrically Distributed Entries
Journal of Statistical Physics
Volume 129, Issue 5-6 , pp 857-884
- Cover Date
- Print ISSN
- Online ISSN
- Springer US
- Additional Links
- Wigner random matrices
- largest eigenvalue
- Industry Sectors