Bulk universality for deformed wigner matrices

J. Lee, K. Schnelli, B. Stetler, H. Yau, Annals of Probability 44 (2016) 2349–2425.


Journal Article | Published | English
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Abstract
We consider N×N random matrices of the form H = W + V where W is a real symmetric or complex Hermitian Wigner matrix and V is a random or deterministic, real, diagonal matrix whose entries are independent of W. We assume subexponential decay for the matrix entries of W, and we choose V so that the eigenvalues ofW and V are typically of the same order. For a large class of diagonal matrices V , we show that the local statistics in the bulk of the spectrum are universal in the limit of large N.
Publishing Year
Date Published
2016-01-01
Journal Title
Annals of Probability
Acknowledgement
J.C. was supported in part by National Research Foundation of Korea Grant 2011-0013474 and TJ Park Junior Faculty Fellowship. K.S. was supported by ERC Advanced Grant RANMAT, No. 338804, and the "Fund for Math." B.S. was supported by NSF GRFP Fellowship DGE-1144152. H.Y. was supported in part by NSF Grant DMS-13-07444 and Simons investigator fellowship. We thank Paul Bourgade, László Erd ̋os and Antti Knowles for helpful comments. We are grateful to the Taida Institute for Mathematical Sciences and National Taiwan Universality for their hospitality during part of this research. We thank Thomas Spencer and the Institute for Advanced Study for their hospitality during the academic year 2013–2014.
Volume
44
Issue
3
Page
2349 - 2425
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Cite this

Lee J, Schnelli K, Stetler B, Yau H. Bulk universality for deformed wigner matrices. Annals of Probability. 2016;44(3):2349-2425. doi:10.1214/15-AOP1023
Lee, J., Schnelli, K., Stetler, B., & Yau, H. (2016). Bulk universality for deformed wigner matrices. Annals of Probability, 44(3), 2349–2425. https://doi.org/10.1214/15-AOP1023
Lee, Jioon, Kevin Schnelli, Ben Stetler, and Horngtzer Yau. “Bulk Universality for Deformed Wigner Matrices.” Annals of Probability 44, no. 3 (2016): 2349–2425. https://doi.org/10.1214/15-AOP1023.
J. Lee, K. Schnelli, B. Stetler, and H. Yau, “Bulk universality for deformed wigner matrices,” Annals of Probability, vol. 44, no. 3, pp. 2349–2425, 2016.
Lee J, Schnelli K, Stetler B, Yau H. 2016. Bulk universality for deformed wigner matrices. Annals of Probability. 44(3), 2349–2425.
Lee, Jioon, et al. “Bulk Universality for Deformed Wigner Matrices.” Annals of Probability, vol. 44, no. 3, Institute of Mathematical Statistics, 2016, pp. 2349–425, doi:10.1214/15-AOP1023.

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