Ajanki OH, Erdos L, Krueger T (2017)
Publication Type: Journal article
Publication year: 2017
Book Volume: 169
Pages Range: 667-727
Journal Issue: 3-4
DOI: 10.1007/s00440-016-0740-2
We consider the local eigenvalue distribution of large self-adjoint N× N random matrices H= H∗ with centered independent entries. In contrast to previous works the matrix of variances sij=E|hij|2 is not assumed to be stochastic. Hence the density of states is not the Wigner semicircle law. Its possible shapes are described in the companion paper (Ajanki et al. in Quadratic Vector Equations on the Complex Upper Half Plane. arXiv:1506.05095). We show that as N grows, the resolvent, G(z) = (H- z) - 1, converges to a diagonal matrix, diag (m(z)) , where m(z) = (m
APA:
Ajanki, O.H., Erdos, L., & Krueger, T. (2017). Universality for general Wigner-type matrices. Probability Theory and Related Fields, 169(3-4), 667-727. https://doi.org/10.1007/s00440-016-0740-2
MLA:
Ajanki, Oskari H., Laszlo Erdos, and Torben Krueger. "Universality for general Wigner-type matrices." Probability Theory and Related Fields 169.3-4 (2017): 667-727.
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